Yes, boys and girls, priestesses and priests, Isis does have a genuine ancient connection with the Winter Solstice. At least by the time of our Greek priest Plutarch, who wrote the famous essay “On Isis and Osiris” in the 2nd century CE. (In fact, he is our source for the most detailed account of the main Isis-Osiris myth.)
Plutarch (his real name, in Greek, is Ploutarchos) mentions a Winter Solstice ritual in which a cow clearly plays the part of Isis:
Moreover, at the time of the Winter Solstice they lead the cow seven times around the temple of the Sun and this circumambulation is called the Seeking for Osiris, since the Goddess in the wintertime yearns for water; so many times do they go around, because in the seventh month the Sun completes the transition from the Winter Solstice to the Summer Solstice.
I used to do a ritual I called “The Isia” when the full Moon occurred on Winter Solstice, which was a meditational “search for Osiris.” Hmmm. I need to find that ritual. It’s so old that I wrote it on a typewriter and don’t have an electronic copy. I’ll have to dig out my paper files.