It seems that you can get different combinations depending on the order you do things. For example, certain hairstyles remove hats, but if you go back into wardrobe, you can put the hat back on (and the hair that sticks out still appears).
Also, TS often tweaks the hair/hat combos. They sometimes release a new hat before they get it to work with 100% of the hairstyles, but then they fix it later. For instance the antlers I have used to make me bald :-O but now I can have them in addition to my pretty hair. I know there was a similar discussion about the cat ears a while ago.
Yesterday I discovered that if I put my top hat on in Wardrobe and then went to Vanity and changed my hair color that the hat disappeared but I was able to return to Wardrobe and put the hat back on. Some hats do not yet work with hair so it is either hair or hat. Some hats work with some hair and not with others. Some hats just do not seem to work with hair at all (haven't tried all styles with each hat). This is not a high priority but eventually maybe all hats will work with at least some hair styles so keep experimenting.
We haven't tweaked this for a little while and right now other work needs to be done before it is revisited. So, for now, some hats don't work with hair- change things up a bit when you are styling yourself to see what else works for you. :)
TS needs to hire a tweaky dev. A dev who just tweak all the little tiny annoying things in the game. Of course that dev would probably get pulled into working on the big things anyways, and then another tweaky dev would need to be hired.
It's a vicious circle. :)
Looking forward to the day I can wear my favorite hair with all the hats that can have hair spilling out from under them.