I have flown with a bird before in the cabin, but yes, the conditions are that you need be be able to fit the carrier under your seat and they need to not be too disruptive. I was flying with my parrotlet Curtis so the carrier size wasn't an issue, but the TSA made me take him out to scan the cage in a room without a roof! He was flighted before the trip but I anticipated they might do that and had his wings clipped for safety safe in the airport and I'm glad I did because it was so scary having to take him out of his cage in such a gigantic, chaotic place (Denver airport)! He thankfully was a good boy and only squirmed and nipped me a little while I was holding him, but the TSA folks can be really unsympathetic to unusual requests like needing an enclosed room. It helped somewhat having us fly during hours where he would usually be sleeping, so he was tired and didn't make a lot of noise. But it was kinda tough.
If you want my advice, I think it would be a good idea to wait until spring to be sure that no big snowstorms interrupt her traveling, either by car or plane.