Yes there are I think they are different according to breed but there are standards. This is from the Rocky Mountain horse assoc. Standard which is what I have :
The horse must have a natural ambling four beat gait (single foot or rack), with no evidence of pacing. When the horse moves you can count four distinct hoof beats which produce a cadence of equal rhythm just like a walk, left hind, left fore, right hind, right fore. Each individual horse has its own speed and natural way of going, traveling at 7-20 miles per hour. This is a naturally occurring gait present from birth that does not require training aids or action devices.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France