Pre-serum Steve had never heard of “deep pressure,” but he and Bucky eventually discovered that if Bucky cuddled him a certain way it really helped when the world got all staticky and stabby around the edges.
Post-serum Steve had the same basic sensory needs (just more stamina for dealing with unpleasant stimuli while still functioning), but less chance of fulfilling them, being stuck in the middle of a war zone without much privacy and also bigger than his former big spoon.
With the Avengers, part of him wanted to ask Thor (you know Thor would give great hugs), but he felt too awkward about it to ever bring it up, at least as of Age of Ultron. Steve and Thor got along well, but weren’t really on snuggling terms, and Steve didn’t trust himself to explain what was, as far as he knew, purely his own peculiarity in ways that would make sense to someone else.
The sad thing is, if Steve had asked, Thor would probably have been happy to oblige him. Thor’s a tactile person, he likes Steve, and he sometimes does something similar for Jane (who is also autistic).