Creation of Magic Hats.
Magic Hats, in the hands of non-casters, have been used to transmit messages.
In the hands of a Hat Magician, a Magic Hat has been used for small object conjuration.
A more powerful version of their hat-based conjuration has been shown to be used offensively, which is referred to as "Pop a Cap".
Creation of Snow Golems
Known Hat Mages
As the traditional use of pulling thing from a hat hints at, Hat Magic is linked to instantanous transport such as portals and could include some type of hammerspace as a natural form of it.
This hints that the possibility of using hat magic to conceal your gems in portals attached to terrain features - hidden trapdoors, if you will. Anything involving (for instance) three obelisks which will open a hidden area if you put a ruby on each and say the magic word "Avalon", would be hat magic. The portal that got the casters out of Gobwin Knob before the volcano erupted would have been hat magic.
Hat Magicians are sometimes referred to by the title of 'Haberdasher.' Most female Hat Magicians go by this title as well, though they may go by the title of 'Millener' if they specialize in making hats for female units.