I'm not sure there's a non distressing or potentially distressing option here, unfortunately. You could try to see if there's a place they could stay that has openings - i grew up with dogs, though so I don't know if there's a kennel equivalent. but that'd be distressing too. I'd suggest looking for a reputable pet sitter who is willing to talk to you about contingencies, but if you want to leave now, its a little late for that.

Yes, its distressing to spend the time in your room, but if they have you, toys they trust, and a little box, you can at least know they'd be safe. That'd be my choice, if my parents were willing to let me do that. I suspect parents will understand that you made this choice because you wanted to be sure you were there for the holidays and will do what they can to accommodate.

But again, I don't have cats, so I'm not sure how these things work that well. Best of luck. Hopefully you won't lose power either way while you are out of the house. I suggest preparing your place best you can just in case, cats or know, which means dripping the faucets and making sure everything is as sealed as it can be. Also, maybe empty the fridge/move it to the freezer. Annoyingly, even if your house dips quite cold, your fridge can still spoil. But none of those things matter as much as your safety.