K.H.
My younger daughter was 2 when we moved and to my great surprise, she did just fine. We didn't have one problem... and we moved 2x within 8 months. (1st an apartment, then bought a house.)
I think that if you make her room and bed the same way with all her stuffed animals, blankets, etc. she will be okay. It might also help her if you don't make a big deal about it. If she sees mommy anxious or acting "funny" she might wonder what is going on (other than the obvious). Another important thing to remember is to keep her bedtime routine the SAME. Don't coddle or rock her anymore than usual until you know how she is going to react.
I think you'll be surprised. Kids are SO much more resilient than we realize. The one I was worried about was my 5 yr old. And she was just fine too. They tend to roll w/ the punches.
Best of luck and I hope it's warmer for the big day! (Our first move was ONE week before xmas!)
~K. =)