Just a small update. I've ordered a starter kit that includes a step motor, small servo and Light dependant resistors.
The kit also has an LCD and some buttons so the time can be changed as you suggested. I know I'll need a heavier servo/motor but my thinking is if I can get it working in principle first I can drop a bigger one into the circuit later.
There's also an IR remote, being able to operate the door using that would be quite handy. I could even get really fancy and have a buzzer go off 10 minutes before the door closes to tell the chickens it's bedtime. They're quite easy to train to that sort of thing. 