Meaning fur was lost before we split from neanderthals, so they would have had to lose their sweat pores and regrown that hair? Seems like a large mutation to take place.
Maybe not as much as you'd think. As an example, the EDAR Gene (https://www.thecrimson.com/article/2013/2/21/sweat-gene-iden...) affects, among other things, hair thickness and sweat gland density. It's isn't a small effect, and yet it's a single gene change in an otherwise highly conserved gene pathway.
Yes - hominims lost their fur before homo neanderthalis/homo sapiens. (Also it's probably more than a single mutation - more like a series of them.)