Fuzzy skull condoms.
Also, for anybody side-eyeing the regionalism “tossle”, it probably originated as a variant of “tassel”? Which, like a pompom, is something frequently worn on the crown of a hat.
What would you call the hat Michael Parks wore in Then Came Bronson?
Toque.
Husband calls them sock hats. Interesting question though.
That’s what the Navy calls them.
I don’t remember ever wearing one as a kid, and I wouldn’t dream of doing that to my hair now.
Stocking cap, ski hat, dorky thing.
Agreed that a beanie is a skullcap that often has a propellor, toboggan is a runnerless snow ride. I know Canadians call it a toque, but that is what a chef wears (and the sign near you is cool). Stocking cap is what Waldo wears, but it gets the idea of being knitted or crocheted across. To be a watch cap, it has to look serious and be dark navy or taupe or something. So I go with stocking cap or knit winter cap. Hat I think of as made of a non-knitted or crocheted fabric, and with a brim.
So we need a do-over with at least all these choices —
Beanie
Bobble hat
Cap
Hat
Knit cap
Knitted hat
Navy watch cap
Pompom
Ski cap
Ski hat
Skull cap
Sock hat
Stocking cap
Stocking hat
Tassel hat
Tobbogan
Toque
Tossle cap
Tossle hat
Tuque
Warm hat
Watch cap
Winter hat
Wool cap
Wool hat
Woolly hat
And pie; one choice should always be pie.
By the way, in my view, “hat” is a misnomer for these things. They’re all caps.
For me, the essentially difference between a hat and a cap is that a hat tends to be more sculpted. That is, it has its own shape, with some degree of permanence. Whereas, a cap is fitted to follow the natural shape of your head. This definition isn’t hard-and-fast, however, because that would make modern professional baseball caps a type of hat.
Yes. A stocking cap.
Toques and beanies and watch caps, forsooth…
I tend towards “winter hat” for simplicity, but have no problem with “knit cap.” “Stocking caps” need a tail and usually a pom pom. “Ski hats” are thicker and usually go lower down on the head. “Beanies” should have nothing to do with this discussion, they have more stiff sides (felt, etc.) and usually aren’t designed with insulation in mind.
I was just reminded that in Indian English this is called a “monkey cap.” Another one for the list!
I have never heard the word “toque” until this thread.
The only time I’ve heard it before was from Bob and Doug MacKenzie. Specifically, their version of Twelve Days of Christmas: “Five gooooolden toooooques!”
A toque is what you pull out of your pocket and pop on your head when your ears are getting cold as you kneel in the snow in front of your car repairing the plug on your block heater from the most recent pull-away damage.
It is a very Canadian thing.
Why ? 
It’s a toque (in a typical Eglish spelling muddle, pronounced to rhyme with ‘fluke’).
There are several styles: stretchy and fits snug to the head; stretchy and fits snug to the head, but has a pom, sometimes on a point of variable size; and stretchy and fits snug to the head, but has earflaps with braids that hang down.
A hat with fur (real or fake) and earflaps that can be pinned up is not a toque; I’m not sure what the official term is, but I think of it as a “Russian fur hat”.
Torques may or may not be fashionable, but they are vital pieces of survival equipment when it is -19C and snowing fine powder persistently on a gusty wind, and you are waiting for the bus to Toronto…
Toque. Why would you want to use two syllables when one will do? 
touche’ 