I just call them winter hats. I wouldn’t call them “knitted”, because most of them in my family happen to be crocheted. Maybe, if for some reason disambiguation were needed, I’d say “yarn winter hats”, but I’m not sure if that’s ever come up.
I think I called them knit hats. But it’s been many years since I lived in a climate in which I wore them.
I’m surprised to have just this moment learned that some people do indeed call these stocking caps. In my dialect, a stocking cap must have a long tapering part that hangs down off the head. A hat that fits tightly to the head can’t be a stocking cap.
I said “stocking cap” because it seemed plausible, but honestly I’d probably call it “that thing, that one there, what you call it.” I barely categorize hats beyond “hat”, and honestly I don’t really consider anything without an at least somewhat rigid shape to be a hat at all. If you pull a woman’s stocking over your head bank-robber style, is that a hat?
Given the relative absence of snow here, that no Aussie kid in history has ever worn a propeller cap except at gunpoint, and finally in Strine the use of latin and french words are *non de rigueur *they are known here without exception as beanies.
Why would you want to use two words when one does the job?