("Joyful" is spelled with one L; "Joyfull" with two L's is incorrect.) No, it wouldn't be a mistake, and I wouldn't notice which word was used. I think they are very close synonyms. They both mean characterized by, or full of, joy. "A joyous holiday season" is not a stock phrase or collocation. It's not like "Merry Christmas," which is. You couldn't possibly say "Cheerful Christmas" or "Festive Christmas" (but could say "Happy Christmas" or "Jolly Christmas.) "Joy," and words related to it, are considered appropriate for the holiday season. Christmas carols contain lines like "Joy to the world," "Tidings of comfort and joy," These perhaps echo the words used by the angel announcing the birth of Jesus, in the traditional 1611 King James translation of the Bible: "Fear not: for, behold, I bring you good tidings of great joy."

I don't know if my non-native opinion counts, but I wouldn't notice whether you said "joyous" or "joyful". So to me it wouldn't be eerie and it wouldn't be a mistake.

Either one would be completely correct. A joyful holiday season implies that many people during that time experience joy, whereas a joyous holiday season implies that the events of the season are inherently joy inducing. So it's really the same thing.