Animals will become disoriented and panicked. You can place them at a location if you have made prior arrangements and have carriers for them. If left alone, they could be crushed in aftershock activity, or run off and eaten by predators. In flood zones they will drown if left confined or tied down. In fires, they may panic and hurt themselves by running into or through fences.
Common problems are burns or broken limbs in horses, colic, and eye irritations.
Fatalities are often from smoke inhalation and any ingestion of chemicals on metal corrals brought to the surface from the heat. This is best done before any disaster. You can train your pet or other animals to come with a word, noise, or whistle by rewarding them with food everytime you present the specific sound. Horses kept out in a pasture should be trained to pen or trailer. They will be extremely stressed if they have to be penned or housed in a stall environment if they are not.