Los Angeles is very a pet-friendly city. Because so many restaurants have outdoor seating, people bring their dogs everywhere, and many stores permit dogs inside. However, if you are renting it will be difficult to find a place that actually allows dogs or cats and you can expect to pay more for the ones that do.
LA also has a lot of areas popular with equestrians and in some neighborhoods you can keep your horse on your property.
Dogs and horses must be registered with the city each year by law. Online registration is available at the Los Angeles Animal Services website
One of the great things about Los Angeles is that the great outdoors are so accessible -- no matter where you live you won't be more than a 30-45 minute drive from nature. However, the American Southwest is home to all kinds of rattlesnakes and the mountains and deserts around Los Angeles are no different.
Rattlesnake bites are common here! For your dog, this is incredibly painful and can be deadly. And for you, this can be incredibly upsetting and expensive: a single vial of anti-venom is $500. When you're out walking with your dog in the mountains make sure you keep your dog on the leash and keep an eye on where your dog is sticking its nose. Rattlesnakes don't always rattle when you approach, and baby snakes don't even have a rattle, so you won't always know you're near one.
As an added precaution, you can enroll your pooch in rattlesnake aversion training. For about $100 your dog will be trained to avoid these snakes based on sight, smell, and sound.
I know, you're probably thinking Los Angeles is in the wilderness...rattlesnakes, coyotes, and don't forget mountain lions and bears. Coyotes are the main animal you need to be aware of if you live near the foothills or mountains surrounding the city. This is particularly true if you have a small dog since coyotes will prey on them. Coyotes are most active during the evening and night, so if you're walking your dog make sure it's on a leash.
Even if you're just taking your dog out for a potty break, keep it on a leash and stay close. Coyotes can swoop in and run off with your pet in seconds.