Did Abraham, David and Solomon think having many wives was sin?

No

Having multiple wives was not a sin back then, as it is not a sin now (outside if it being illegal).

History

At the time of Abraham, David, Solomon, and Jesus, polygamy was part of the culture.

Even in Jesus' times, polygamy was allowed and part of the customs of the Israeli people. The historian Josephus noted that Herod was allowed to have multiple wives, because it was the custom in Israel at that time.

Furthermore, it was allowed per the Bible. When God gave the commands to Moses, he gave special instructions for the situations of multiple wives:

Deuteronomy 21:15-17
15 If a man has two wives, and he loves one but not the other, and both bear him sons but the firstborn is the son of the wife he does not love, 16 when he wills his property to his sons, he must not give the rights of the firstborn to the son of the wife he loves in preference to his actual firstborn, the son of the wife he does not love. 17 He must acknowledge the son of his unloved wife as the firstborn by giving him a double share of all he has. That son is the first sign of his father’s strength. The right of the firstborn belongs to him.

Had God detested polygamy, there would have been a command against polygamy. By comparison, God said that Kings shouldn't take too many wives so that his heart isn't lead astray, which is a further command showing that polygamy was allowed.

Side Note
That laws preventing polygamy began with the pagan traditions of the Roman Empire. It wasn't until 300 years after Christ that Christianity united itself with the Roman traditions. It was then that polygamy became outlawed.

Summary

Historical and biblical evidence shows that polygamy was common practice and acceptable in the site of God and the people during the time of Abraham, David, and Solomon. Their polygamy was not a sin, just as it is not now..

As usual, my answer is long-winded, but it is, I hope, worth reading nevertheless. In answering many such questions, we need to take the long view, so to speak, and treat an important issue such as this one in the context of the entire canon of Scripture, which we today--unlike the saints of old--have the privilege of possessing in its fullness.

Did Abraham, David and Solomon think having many wives and concubines was sin?

Probably not. The three personages you cite were all very wealthy men, and they could afford multiple wives. Keep in mind, however, all three men were responsible for the well being of each wife and was "legally" married to her for life. We need to divest ourselves today of the notion that the marriage of a wealthy man to a woman of his choosing was a trivial thing back then; it was not.

To a lesser extent, the "husband" of a concubine was also responsible for the well being of his "property," since in Old Testament times, a concubine was often a slave, as well as a "mistress" and/or a provider of children to a man whose wife (or wives!) could not have children. The "Got Questions" website is helpful in this regard.

God's design from the beginning was for a man to leave his parents, cleave to his wife (singular), and become one flesh with her. Becoming one flesh with a wife, then and now, involves more than just sexual consummation; it is an expression of physical, psychological, and spiritual intimacy. Moreover, and most significantly, from the very beginning marriage prefigured the union of Christ with his church. His bride.

"This mystery [of 'one flesh'] is great; but I am speaking with reference to Christ and the church. Nevertheless, each individual among you also is to love his own wife even as himself, and the wife must see to it that she respects her husband" (Ephesians 5:32-33 NASB Updated).

As a Christian author pointed out to me recently (sorry, I can't provide the citation), the "mystery" to which Paul alludes is not that God used marriage as an analogy for Christ and the church, but that God used Christ and the church as an analogy for marriage. There is a significant difference between the two.

God's plan from eternity past was to provide a bride for His Son, so that Jesus would be the "firstborn among many brethren." God, the Father of the only begotten Son of God, could think of nothing more delightful than for His heaven to be filled with a people who would be conformed to the image of His Son (see Romans 8:28-30). One day, that people-group, comprised of every tongue and tribe and nation ("living stones," as it were) will comprise

"a spiritual house for a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ" (1 Peter 2:5).

God, then, set the standard of care of a husband for his wife very high indeed:

"Husbands, love your wives, just as Christ also loved the church and gave Himself up for her, so that He might sanctify her, having cleansed her by the washing of water with the word, that He might present to Himself the church in all her glory, having no spot or wrinkle or any such thing; but that she would be holy and blameless" (ibid., vv.25-27, my emphasis).

As for the church being Christ's bride, we need only look to the Revelation of Jesus Christ:

• "'Let us rejoice and be glad and give the glory to Him, for the marriage of the Lamb has come and His bride has made herself ready'" (Revelation 19:7 NAS).

• "Then one of the seven angels who had the seven bowls full of the seven last plagues came and spoke with me, saying, 'Come here, I will show you the bride, the wife of the Lamb'" (Revelation 21:9 NAS).

• "The Spirit and the bride say, 'Come.' And let the one who hears say, 'Come.' And let the one who is thirsty come; let the one who wishes take the water of life without cost" (Revelation 22:17 NAS).

How is all this related to Abe, Dave, and Sol? In every way, as it turns out! Let's first switch gears.

When some Pharisees attempted to test Jesus by asking him

"' Is it lawful for a man to divorce his wife for any reason at all?'" (see Matthew 19:3),

how did Jesus respond to them?

"'Have you not read that He who created them from the beginning MADE THEM MALE AND FEMALE, and said, 'FOR THIS REASON A MAN SHALL LEAVE HIS FATHER AND MOTHER AND BE JOINED TO HIS WIFE, AND THE TWO SHALL BECOME ONE FLESH '? So they are no longer two, but one flesh. What therefore God has joined together, let no man separate'" (ibid., vv.4-6, my emphasis in italics).

When the Pharisees continued their testing of Jesus by asking him

"'Why then did Moses command to GIVE HER A CERTIFICATE OF DIVORCE AND SEND her AWAY?'" (ibid., v.7),

what did Jesus say?

"'Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way'" (ibid., v.8).

Putting all these scriptures together, I suggest the following:

1. God's will for Abraham, David, and Solomon (and all the other polygynists mentioned in the Old Testament) was for them to have one wife, and one wife only.

2. Just as Moses (note well: not God, but Moses) permitted divorce because of the children of Israel's hardness of heart, so also did God permit the patriarchs and saints of old to marry more than one wife. Polygyny was not God's will, but he permitted it, not necessarily because of the hardness of heart of Abraham et al., but because of their ignorance of the true significance of marriage in God's eyes.

3. In Old Testament times, many women were--at best--third-class citizens with few if any of the rights which women today take for granted. Becoming a second (or third, or fourth, etc.) wife or concubine was perhaps an unappealing option back then, but it was better than being destitute or being forced to turn to prostitution to avoid becoming destitute. Today, women have the opportunity to further their education, receive specialized training, acquire a trade, and so much more. Moreover, divorce laws make it possible for a divorcee to receive help financially until she gets back on her feet after a divorce. There are also many other laws protecting women today that women in David's and Solomon's day could only dream of!

4. As God's revelation of his will increased and progressed, becoming fuller through new revelation (which peaked, so to speak, in the writings of Paul on marriage, for example), God commanded that leaders in the church (both elders and deacons) must be the husband of only one wife . In other words, they are to be "one-woman men" (see 1 Timothy 3:1-13

We do well to notice, moreover, that in virtually each and every instance of polygyny in the Old Testament, disputes, conflict, hard feelings, and complications of all sorts resulted. If someone reading this answer can supply an instance when multiple wives was not fraught with any of the negatives I've just cited, I'd be interested in knowing about it!

In conclusion, did Abraham et al. think their taking more than one wife was sin? Probably not. Was it God's will for them? No. Evidently, however, God was gracious in overlooking their behavior, which proceeded from their ignorance of his "good, acceptable, and perfect will" for them (Romans 12:2b). God also allowed polygyny and concubinage to exist back then out of compassion for women who were by and large held in such low esteem in male dominated cultures. I'd like to think, however, that most polygynists who were also believers in the one true God of Israel treated their multiple partners better than the unbelievers and idolaters in the nations surrounding Israel.

Today, Christians cannot plead ignorance as an excuse for taking more than one wife. Their excuse--really, a rationalization--simply will not hold water.

A final thought. If the member of a primitive tribe in the Amazon Rain Forest becomes a Christian, and he has multiple wives, how would you advise him?

There were specific instructions for the king of Israel to not acquire many wives for himself, since that could have the effect of turning his heart away from the Lord. This text predates the first king of Israel, so I would say that David and Solomon should have known that this was forbidden.

(Note: the Bible did not actually forbid them from polygamy, but from having a whole bunch of wives.)

"When you come to the land that the LORD your God is giving you, and you possess it and dwell in it and then say, 'I will set a king over me, like all the nations that are around me,' you may indeed set a king over you whom the LORD your God will choose. One from among your brothers you shall set as king over you. You may not put a foreigner over you, who is not your brother. Only he must not acquire many horses for himself or cause the people to return to Egypt in order to acquire many horses, since the LORD has said to you, 'You shall never return that way again.' And he shall not acquire many wives for himself, lest his heart turn away, nor shall he acquire for himself excessive silver and gold. Deuteronomy 17:14-17 ESV

As for Abraham specifically, aside from the affair with Hagar, he stayed married to one wife (Sarah) until she passed, after which he married Keturah and had children with her.

The Bible does not explicitly state that polygamy was forbidden, yet it would have been instructive to note that God created Adam and Eve--not Adam and Eve and Shirley and Tina and...