Word for covering yourself with something while slouching?
Solution 1:
Perhaps huddle
Curl one’s body into a small space: the watchman remained, huddled under his canvas shelter
Oxford Dictionaries Online
and
To draw or curl one's limbs close to one's body: huddled under the blanket while watching television.
American Heritage
Solution 2:
[Since I was beaten to huddle...]
hunker
Bend the top of one’s body forward; hunch
It's often used with down:
"We walked through the snow, hunkered down inside our coats."
Solution 3:
Snuggled
We walked through the snow, snuggling under our coats.
The term snuggle is more commonly used in the following: "to snuggle under the covers/blankets" but there's nothing to suggest that the protagonists cannot snuggle while they wrap themselves in their coats. Alternatively...
We walked through the snow, wrapped in our coats.