Carey, 41, also uploaded a photo of herself with Cannon from inside his Aspen, Colo., hospital room.
"We're trying to be as festive as possible under the circumstances but please keep Nick in your thoughts because this is very painful," she wrote on her official website, adding that doctors tried -- and failed -- to remove her from Cannon's room.
"We're doing OK but we're stranded in Aspen," Carey added. "I know, we could be in a lot worse places, but the truth is as long as we're together, we're OK."
"I'm not trying to make light out of the situation because it's a serious moment that's very tough on all of us," Carey, mother to twins Moroccan and Monroe, wrote. "So please keep us and our family in your prayers."