On an iPhone SE, which is not in the device drop-down.
Leashed horses (and donkeys and mules) will not jump when faced with a 1-block jump. Instead they seem to treat the block like a fence, and will stand there until the lead breaks. An exception to this occurs when the horse starts walking before being pulled uphill, Going up a 45-degree slope also works, but in this case the horse is being dragged uphill. Leashed sheep, cows, etc jump just fine.