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.