Fur hats were very common in the “early modern” era. In fact, they almost led to the extinction of many animals whose fur was used. They starting falling out of fashion in the west in the 19th century (when a picture circulation of Benjamin Franklin with a “spodik” became popular in Paris during the revolution, Franklin who would never be caught dead in one when living in Philadelphia sent a rush order for some and used it as a trademark).
Most of “cool” stories about their origins are probably folk-myths (but they are “our” folk myths, and warrant respect).
If fur hats were still popular in America, the Modern Orthodox anti-hasidim wouldn’t be complaining about them and pretending its a religious-based objection, rather than complaining that Boro Park doesn’t follow the same fashion Gurus as Manhattan.