There is a lot of info if you search for "chicken coop door" believe it or not here ETO and AAC. You can also look for automatic dog dishers.
A possibility that might exist for use is a grain auger, a weight sensor and a door. I'm assuming food or hay.
The horse is pretty strong. You might look at linear actuators. the simplest, non-web based is linear actuator, limit switches and an astronomic timer. With those timers you can set times like 1 hr after sunset ON and 11:30pm OFF.
"smart relays" such as manufactured by idec may be useful. The problem becomes power and time-keeping. Solar might be an option.