The general consistency varies, but it can be anywhere from fairly creamy to milky or watery, it differs depending on the sperm count.
Horse semen shots were actually popularised 4 or 5 years ago in New Zealand, and they're described as tasting almost like a milkshake, which is laughable, but hey I haven't personally tried so don't take my word for it
so far as semen from various mammals go horses are definitely one of the more widely appreciated, generally fairly salty/sweet due to a very high protein content, very musky too.