J.,
My son, now 2, is very much like this. We've always had stuffed animals around him but he never wanted them. Since we didn't have a blanket in his crib when he was little, he's also against having that in his crib, let alone covering him.
Thankfully he's never had a problem putting himself to sleep but he's also never been one to cry it out (he would literally cry for hours if we let him) so whenever he'd wake up upset, it was always very difficult to calm him. Usually picking him up would calm him but getting him back into bed was another story.
Every once in a while he'd wake up upset and would almost act as if he wanted us but was afraid of us. He's reach for us and then back away in the corner of his crib, or in the corner of his room and just scream and cry. It was always heartbreaking as we just didn't know what to do. My husband has always been able to calm him when I couldn't but during these episodes, sometimes that didn't even work. I still don't know what caused this -- maybe he was getting sick or teething, etc. I don't know. Walking around the house, doing something with a change of scenery was the one thing that would eventually calm him down -- but only if my husband did it.
Going off on a tangent now...
Towards the end of the summer, I knew I had to get my son used to a blanket so he wouldn't freeze in the winter. I started off with a very lightweight receiving blanket with cars on it. We talked about how cool the blanket was before bedtime and got him excited about it. He let us keep it in the crib that night but when we looked in on him later and tried covering him, he woke up (super light sleeper) and threw it off saying 'no'. Every night we kept talking about sleeping with the cool car blanket and we told him 'yes'! He's going to be covered. This took awhile but he loves his blanket now. We also bought him a Fleece Thomas the Train blanket that he can't sleep without now (and covered!). Since then, he's slept much, much, much better and I don't think we've had a single episode of him waking up upset.
Good luck.
-Jen