Do Latter Day Saints / Mormons consider themselves to be henotheists?

No. We have one God. "Him only shalt thou serve". Search the Scriptures; they all testify that this is true. We keep this commandment.

It is true that the children of God have the potential to grow up to be like Him through His power, because of Jesus Christ. Otherwise the terms "children" and "Father" would be utterly meaningless, making the Scriptures null and void. God is not a liar, therefore we are His children, and we can be like Him. All of the Scriptures point to this fact.

Does the fact of any of God's children becoming as He is mean that we have more than one God? Absolutely not!

We have one earthly father, and the commandments say we are to honor our earthly father. Is my earthly father the same as your earthly father? I trow not! Is that same honor due to someone else's father from us? Of course not! Otherwise God's Creation of Families would be worthless and meaningless also. But God is a God of order. He does nothing that is worthless or meaningless. The Family is ordained of God. It is made in the likeness of the Heavenly Family, and is a tutor and a place to practice Celestial relationships, not a civic bond to be dissolved or escaped. "What God hath joined together, let no man put asunder." This warning is as stern as eternity. This life is a nursery for eternity.

Just as each child has exactly one father who begot his body, and to whom obeisance is due, so too each spirit child has exactly one Heavenly Father, to Whom all worship, honor, and glory is due. This is simple, and anyone who keeps the commandments is capable of understanding it.

We have one God, our Father, and we can be like Him through the merits of His Only Begotten Son, because we are also His spirit children. Otherwise there is no Scripture.

Normally, you would expect that polytheism or henotheism implies not only the existence of other Gods, but that these Gods also influence things on earth, or can be prayed to. Something like that. Seen in this light, I'd argue LDS theology is not poly- or henotheistic.

LDS theology sees God the Father, God the Son, and the Holy Ghost as three distinct beings. Does this mean polytheism? I'd argue no, because being one in their goals etc. means that, for example, praying to the Son you will not get any different outcome than praying to the Father. Functionally, this is the same as having a trinity, just without the mystical union stuff. Having patron saints for different stuff like catholics do is much more polytheistic in my eyes, even if they are not called "Gods".

LDS theology says we can become like God, and in extension it is believed (though I am not sure how much this counts as doctrine) that God was once like us. This creates an infinite chain of Gods both in the past and into the future, and we are somewhere in the middle. Is this poly- or henotheistic? I'd argue no, because even if there exist other Gods, none of them have any bearing on our life on Earth. This is more akin to saying that there is stuff outside of our observable universe. Most likely true, but none of that stuff will or can influence us. Trying to pray to whatever other God there might be would be the same as praying to an Idol.

You could say that in some sense out theology follows the principle of mediocrity, in that unless revealed otherwise, we have to assume that what we go through here on earth is normal, happens everywhere, has happened forever somewhere, and will happen forever somewhere.

The Church of Jesus Christ of Latter-day Saints' official website explains how their Church may have both monotheistic and henotheistic aspects. It states,

"For some observers, the doctrine that humans should strive for godliness may evoke images of ancient pantheons with competing deities. Such images are incompatible with Latter-day Saint doctrine...Latter-day Saints also believe strongly in the fundamental unity of the divine. They believe that God the Father, Jesus Christ the Son, and the Holy Ghost, though distinct beings, are unified in purpose and doctrine."

The entire article is a few pages long and may be accessed here: https://www.lds.org/topics/becoming-like-god?lang=eng

No, the Church of Jesus Christ of Latter-Day Saints is not Henotheistic. This will be clear by comparing what members believe with what Henotheism means (see below). We don't choose a god to worship. We worship God. We clarify who we mean by saying "the Eternal Father" or "Heavenly Father".

The Church of Jesus Christ of Latter-Day Saints - Godhead

We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost. - Articles of Faith 1:1

This topic goes into more depth about what we believe about the nature of God:

They acknowledge the Father as the ultimate object of their worship, the Son as Lord and Redeemer, and the Holy Spirit as the messenger and revealer of the Father and the Son. But where Latter-day Saints differ from other Christian religions is in their belief that God and Jesus Christ are glorified, physical beings and that each member of the Godhead is a separate being. - Topics: Godhead

Henotheism

A henotheist may worship a single god from a pantheon of deities at a given time, depending on his or her choice, while accepting other deities and concepts of god. - Wikipedia: Henotheism