In a wetter environment, it's not uncommon to see horses standing out in the field with ice on their back. Or even snow, if it's been snowing.
Horses are adapted to fairly cold weather. They produce a nice, thick coat in winter, unless humans interfere with the process. A horse that's grown sufficient coat is so well insulated that any snow or ice that ends up on them, either from falling or from them rolling, will stay there until it melts. It doesn't bother them at all. (In Iceland, horses are the only livestock that don't spend the harsh winters inside!)
In fact, the rule of thumb some horsemen use is that if the horse does not have ice or snow on their back in these conditions, the horse probably needs a blanket.