Because they look silly in sport coats.
And don’t even get me started on muumuus.
We blanket our show horses - prize winning halter competitors, through the winter. We do it because we live in a cold climate (Wyoming) and we have some winter and early spring shows, including some lucrative stallion expositions (where we can sell breeding fees). A properly blanketed horse doesn’t grow a winter coat. A shaggy horse doesn’t show its composition or definition very well. A shaggy horse doesn’t win shows or get as many breeding fees. If we didn’t blanket our show stock, we wouldn’t be competitive until June.
BTW, our non-show stock are in the cold Wyoming winters unless it gets around 10 below or so, and are no worse for wear. Brood mares are sheltered come early spring if they are in foal.
Oh, we also blanket horses on the way to shows or expos no matter what time of year. We spend about an hour and a half washing and grooming our horses before we start to travel to a show. It helps maintain the grooming until we arrive, so when we do our on-site grooming we aren’t starting at square one. (It still takes another hour of on-site grooming, however.)