Spiritual significance of hats?

Now, I know a lot of religions have traditions of head coverings, either in general or during worship, but I'm wondering if there's a non-religious spiritual dimension we've overlooked. I was just out walking my dog. I saw many of the folks I usually see, but, since the day is cold, and I had a hat on, I tipped my hat instead of waving. Now some of the reactions may have been smirks at an obsolete gesture, but I felt the majority of people were pleased and warmed in a way that my mere hand waves never accomplished. What facet of the human spirit might account for this?