First off, when is your winter break? If it's before February, you will probably be okay. If it is after February, and US files for Chapter 7 (which seems more and more likely by the day), UA
will most likely protect you on other flights.
What's your itinerary? If it's something that UA
flies with their own metal, they will, almost guaranteed, put you on their own flights. UA
may not be in the greatest financial situation, but they aren't going anywhere at the moment.