??? No, they don't. They only smell bad when they're kept standing in their urine, which is still not worse than a hairdresser. Compared to dogs (or ICE cars) horses smell way less. They do sweat to regulate temperature, which has a distinct smell, but it's way less irritating to a human's nose than the sweat of the rider.

There's a set of distinct smells associated with the horses, but other than the piss, none of them are particularly "bad". In my experience, humans tend to smell way worse overall (from food to body odor to the excrement) than horses.