Notice that he's in the exact same clothes, the black sweater. And there is nothing over him. There was definitely nothing over him.
Now, here he is being unloaded at Parkland, being removed from the ambulance. But, now he's got a blanket or something over him.
Where did that come from, and how did it get on him? Here's another view of it. Notice that they didn't cover his legs. If they had covered him trying to keep him warm, they would have covered his legs as well.
Oswald was definitely uncovered when he was put into the ambulance. But, he came out of the ambulance covered with something. Explain that. Somehow, Oswald got covered in transit, and I don't like it.