Yes, but not in the same way we do. Because horses don't breathe through their mouth, they don't produce the kind of explosive sneeze a human can. A sneeze is often mistaken for a snort or a "blow" (which I explained yesterday).
They do sneeze, though, and for the same reason - dust or some foreign body in their nostrils, or clogged sinuses. It's not uncommon for a horse to sneeze a couple of times when pulled out of a stall and put to work - they're just clearing their airways. Needless to say if a horse is sneezing a lot, or sneezing when they don't normally, then they may have something going on such as a respiratory virus or allergies.