Does "beanie" = "watch cap"?
I find there's enough elasticity in a stretched-to-wear watch cap that its coming off has never taken place, and I must have occasionally put one on right after a shave. I do pull it down firmly and don't wear it heavily brim-rolled, perched like a pancake, covering just a bit of the top as I sometimes see them worn, although not by sly-types.
In Ming's lexicon, a "beanie" is what a Cub Scout or a cardinal wears as part of his uniform/regalia.
Now, I have had a bit of trouble with (borrowed) yarmulke slippage at Passover when asked to a Seder, but wind is usually no problem around the Passover table (except briefly when the door is opened for Elijah to come in).