hiya, yes they certainly can - i have seen horse's with sweat rashes after heavy work with dirty, greasey or sweaty saddle cloths on, that has been followed with no washing down on a really hot day or even a brush down.  Some horse's can get lumps on their back, girth area (general saddle area) but i knew a woman who used to put rugs on her horse in the summer (...she was a class A fud...literally) and he used to get bald patches because he would sweat up to a horrible extent...she was such a fud, i cannot actually get over her fuddiness - don't you just HATE stupid people like that?!  Big rugs on the horses in the summer so they don't get dirty?!  WTF?!  CRAZY!

but yes, they are possible