Eventually you can jump through fire! (Or try to...)
jumping, you will begin with a set of cavaletti trainers. These are short poles just a few inches off the ground which are used (in real life and in Sims 3) to train both horse and rider in the fundamentals of jumping. As with all jumps, you can either buy some and set them up on your home lot, or you can go to the Training Center and use the equipment there.
The jumps themselves come in several different varieties and level of difficulty. The most difficult jump is the Ring of Fire, which is apparently also somewhat dangerous!
It seems that the sleep cycles of horses and their owners are always out of sync. Luckily, both horse and owner can train independently! You can control your horse then click on the jumps to have your horse train to improve their jumping skill. When the horse is asleep or exhausted, you can train your Sim either by having them read the Riding skill books or by taking classes at the Equestrian Center rabbit hole.