This is how one would speak to a baby or a small child. This one in particular seems to come from the saying, "Snug as a bug in a rug", which is a phrase a parent would say after tucking a child into bed.

It's baby talk

It is someone trying to imitate in text how you might talk to a small child or baby. I would assume that the meaning is just that something is snug and warm. For example you might cover a baby with a blanket and then do that cute (?) baby voice awwww...is baby all snuggly wuggly?