Hint — there are no Classical period Hellenic religious festivals (at least in the Athenian Festival calendar) to mark the Winter Solstice. The closest we come is a modern festival called Heliogennia. The reason for this, at least in my opinion, is that the winter solstice was not as important to the Greeks in the Classical period as the sea storms that Poseidon was called upon to mitigate during this time.
However, the polytheistic peoples of the time would trade with other areas and would honor the Gods of the places they went to along with their own. In Athens, the “Alter of the Unknown God” potentially looked similar to this illustration:
BUT it was not dedicated strictly to a SINGULAR God, instead being dedicated to all “foreign” Gods no matter where those Gods were originally worshipped.
Because of this, as a Hellenic Polytheist, I don’t actually see any conflict between my faith and adding the “foreign” festivals such as Yule and Christmas — as long as I recognize them as such, and also recognize that Christmas has both secular and religious components. To a child, the “Christmas” specials (such as “Rudolph the Red-Nosed Reindeer” and “Frosty the Snowman”) are not always religious in nature, but are still magical. Even the Disney Jr. Channel offerings are secular.
So, we will have a tree and wreath as well as doing the gift-giving on Christmas Day. We will offer religious thanks on the Solstice (Heliogennia). And, most importantly, we will not assume that our traditions are the only ones worth celebrating….