Carey, 50, teamed up with Grande, 27, and Hudson, 39, on a remix of the 2010 single and released a music video for the song Friday.
The new video shows Carey, Grande and Hudson perform on a Christmas-themed stage. The trio are joined by backup dancers dressed up elves.
The original "Oh Santa!" appears on Carey's holiday album Merry Christmas II You, released in November 2010. The new version is featured in Carey's Apple TV+ special, Mariah Carey's Magical Christmas Special, which premiered Friday.
Carey's Apple TV+ special features Carey, Grande, Hudson, Tiffany Haddish, Snoop Dogg, Misty Copeland, Carey's 9-year-old twins, son Moroccan and daughter Monroe, and other special guests. The special features songs from Carey's holiday catalog.
Carey said Thursday on Good Morning America that the special was her way of "pushing through" the difficult year.
"I'm saying this from the heart. I wouldn't feel happy if I couldn't celebrate with fans this year," the singer said.
"And just with the world, it's just been so traumatizing what's happened this year. But I think pushing through, and the way things are kind of changing for the better, pushing through with this holiday season for me was super important," she added.
Carey celebrated the 25th anniversary of her famous holiday song "All I Want for Christmas is You" in 2019.