R.
My daughter is exactly the same way! It drives me nuts. She just turned 2, but she has never liked sleeping under a blanket. (She also refuses to wear any kind of sock or shoe, so I am batteling that as well). My daughter sleeps in our room, so I am up covering her 2 or 3 times a night. Not the best solution, but I don't sleep well anyway, so it works for us;) On the other side of the coin, my oldest daughter sleeps completely covered from head to toe and I have to go in and uncover her face a couple times a night so she doesn't smother. Oh well... Good luck.