The Origin of the Santa Hat
1. The traditions associated with the Santa Hat are descended from both sun worship and the Saturnalia. This is a reflection of the fact Christmas is descended from both Mithraism and the worship of Saturn on his day: the Saturnalia.
2. The Santa Hat was known as the Pileus, Cap of Liberty, and Freedman's Cap at the Saturnalia. It was known as the Phrygian Cap and Cap of Mithra in sun worship.
3. This hat was certainly used in the worship of the sun.
4. This cap is still worn on one of the two most important dates in sun worship ritual: the winter solstice which coincides with Christmas.
5. This hat was worn by the priest in sacrifice, hence the blood red color.
6. The populace only wore this hat at the Saturnalia. This coincides with how the populace wears the hat today. It is worn at the same time of year at the same festival. Only the names have changed. The Saturnalia is now known as Christmas and the Pileus is now known as the Santa Hat.
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.