Universalism in the Orthodox Church?

Yes and no. In historical Christianity, the term for universal salvation is apocatastasis. Apocatastasis refers to the restoration of all things to their original state, which includes the notion of universal reconciliation (even going so far as to insist that Satan himself will eventually be reconciled to God). The word appears in Acts 3:21.

"Repent therefore, and turn back, that your sins may be blotted out, that times of refreshing may come from the presence of the Lord, and that he may send the Christ appointed for you, Jesus, whom heaven must receive until the time [(this is actually plural in the Greek: 'times')] for restoring [(apocatastasis)] all the things about which God spoke by the mouth of his holy prophets long ago" (Acts 3:19-21).

Since this isn't the Biblical Hermeneutics Stack Exchange, I won't get too crazy on the exegesis of this passage but it must be noted that there is an alternate way to translate it. The word "things" is implied in πάντων in the above translation, but the relative pronoun (ὧν) could be referring to 'of times' (χρόνων). The argument boils down to whether there will be a restoration "of all the things about which God spoke" (as rendered in the above translation), or if there will be a restoration "of all the times about which God spoke." This alternate translation may be responsible for some of the early speculation about apocatastasis.

1 Corinthians 15:28 has also historically been used as a justification for apocatastasis:

"When all things are subjected to him, then the Son himself will also be subjected to him who put all things in subjection under him, that God may be all in all."

Scholars are still divided on where this teaching originated, most pointing the finger at Origen. It is debated whether or not Origen taught apocatastasis and whether this even implied universal salvation. It was certainly a very common belief among many early Church fathers, however. Origen is said to have been posthumously condemned at the 5th ecumenical council along with his belief in apocatastasis as universal salvation. Therefore it is commonly taught that the official teaching of the Christian Church is that universal salvation is heretical. However, many scholars have questioned whether apocatastasis was actually condemned. Origen was also condemned for a number of beliefs he held that were Platonic (such as the preexistence of souls, a heterodox Christology, animistic beliefs, etc.). Scholars have debated whether it was the Platonic foundations that he mixed with apocatastasis that were rejected or the entirety of the doctrine itself. There is significant evidence that suggests that many have misunderstood what was specifically denounced in the 5th council.

The idea as presented by Origen is that since God will be "all in all," then in eternity there will be no place that God is not. Since "God is love" (1 John 4:8), wrath is not an eternal attribute of God but rather how we experience His love without being pure in heart / righteous. Therefore hell is not viewed as conscious torment inflicted intentionally by God as punishment nor as a withdrawal of God's presence, but rather as the experience of the unfiltered love of God. For those who have been made righteous, this is a very positive experience. For those who have chosen to reject His love, it is like a consuming fire that causes them suffering. Origen taught that this fire was purifying and that eventually no one would hold out against God's love. Origen believed that all would eventually be reconciled to God.

Some have stated this by using the analogy of wind: God's love is like wind constantly blowing in one direction. When we walk in His will, the wind has our back and carries us along. But when we go against His will, we walk against the wind and experience His love as wrath. Thus God is always continually loving, but we are the ones who don't know what true love is. This can even be observed in human relationships: consider a loved one who hates a family member. Let's say that Helga is the mean and bitter loved one and Cindy is the kind relative. Helga intentionally buys Cindy a mean gift on Christmas - something that Cindy finds offensive. Cindy knows that Helga will be mean but chooses to love her anyways and purchases a thoughtful gift for her. When Helga opens the loving gift from Cindy, she throws it on the floor in anger and shouts, "You did this on purpose!" Perhaps this is even the key to understanding how God's love can be like "heaping burning coals on someone's head" (Proverbs 25:21-22; Romans 12:20). Many Eastern Orthodox believers view God's love in this manner. Many in our broken culture experience true love as a form of suffering. Orthodox Christians believe that eternity will be no different, since God is always love. This is basically the Orthodox doctrine of 'hell' in a simplified (albeit incomplete) way.

But what about universal salvation? It may be true that people will experience God's love as suffering, but will this experience be eternal? Do Orthodox Christians believe that all will be saved?

We must also consider another great saint who taught apocatastasis but was not condemned for it: St. Gregory of Nyssa. St. Gregory of Nyssa was one of the Cappadocian fathers who repudiated the Platonic teachings of both Irenaeus and Origen. Yet he never repudiated the teaching of apocatastasis, although he did modify it slightly. Since St. Gregory of Nyssa was never condemned as a heretic nor any of his teachings, it is often thought that perhaps apocatastasis is not heretical, but rather the way that Origen had presented it and infused it with Platonism was the problem (technically neo-Platonism for those philosophy/history buffs reading this). Add to this the fact that universalism may not have even been specifically addressed in the 5th ecumenical council and there is a valid argument that this view may not have been considered heretical by the early Church (cf. this, this, and this).

These beliefs can be seen throughout both Eastern and Western Christians through the medieval period, all the way up until the Reformation in the West. This hope for an eventual universal reconciliation has continued in much of Eastern Christianity - but not in any dogmatic way (this would be counter to the Orthodox approach to theology, which is a discussion for another time).

Of course you can find Orthodox Christians who vehemently support either extreme, but you can also undoubtedly find Universalists within mainline conservative Protestant denominations as well. The presence of alternate opinions does not imply agreement from all those within a tradition. There are also many underlying related concepts that I do not have time to sufficiently address, such as the notion that heaven and hell are 'places' that exist within space and time, the apophatic approach to theology, and much more.

The best way to summarize the position of the Eastern Orthodox Church is perhaps to say that they hold out hope for the eventual reconciliation of all to God. Thus it would be heretical to say that all will be saved, but it is legitimate to hope that all may be saved.

Here is a scholarly article tracing Patristic teachings on apocatastasis.