The Santa Hat as we know it "only" goes back to the 18th Century. Our Santa ideal is still based mostly off of Victorian ideals of Santa - the actual story of Santa being as old as the Bishop himself. :-)
Since Santa is supposed to be a grandfather like figure, he's wearing clothing associated with grandfathers of the Victorian era - that old style (18th Century and very early 19th century) nightcap with an older styled suit. The traditional Santa hat is based of a men's nightcap. The term nightcap doesn't mean it was used just for sleeping - both men and women wore them inside their own homes. You wouldn't necessarily wear it outside of your house those - like Pajama bottoms. Unless you want to be labeled the modern term of "People of Walmart", you aren't wearing your nightcap outside.
However, Santa gets a pass because every home is his home. We lay out a meal just for him - of milk and cookies- and he is free to wander from house to house as if all are his. So, yes, there is a bit of deeper symbolism in the traditional Santa hat. :-)