Awww Gwen, I am jealous. DH never tries to cuddle up to me in the middle of the night. He gets really hot at night (he has a sheet over him while I have the regular doona) so he doesn't like a lot of snuggling. Apart from the fact that he is about as affectionate as a rock lately, he hasn't snuggled up to me since we were first going out.
Come to think of it though, I would push him away after a while because I do need my space in bed so perhaps I conditioned him in some way?

Still, I wouldn't be worried about pushing your DH away - so long as he doesn't take it personally and realises that it's just your "asleep" reaction. We all need our space, right?