Horses cannot walk up staircases or walk through 1-width gates, but may take a taxi boat. Horses can be placed in horse box stalls or tied to hitching posts to fulfill many of their motives.
Sims can ride horses if they have a high enough riding skill, and may do so autonomously if they have a good relationship with the horse. Foals are closely attached to their mothers, and both will panic and become unhappy if they are separated. Horses can WooHoo with each other to breed and produce offspring. There doesn't seem to be a way to discourage or remove this behavior, so the best way to combat it is to keep plants in a fenced-off area with a single tile gate (which horses are unable to go through).
Horses and unicorns, both tame and wild, will eat most gardening plants, destroying them. Horses are closely connected to unicorns, and can breed with each other. Horses can either be wild horses that roam around the world, or tamed horses that are part of the active household. They can befriend human Sims, dogs, and cats, and can use all interaction types with them except romantic. Horses are controllable like dogs and cats in The Sims 3.