Do "horse latitudes" have anything to do with horses?

Possibly - and possibly not. One folk etymology for the term is that when ships became becalmed at these latitudes, which happened a lot, some of the horses being transported would die.

However, a much more likely explanation is that seamen did something called the "dead horse" ritual when they had received enough money to pay off their debt to the paymaster for the last shore leave - they would make a straw-stuffed horse effigy, parade it around the deck and then throw it overboard. West bound shipping from Europe would hit this point in the subtropics.

The ritual came from the saying "to beat a dead horse."