That's a tough one. If it is the kind you haul up on a chain....there is little for them to bother with..
But If it is a smaller one and the tracks hang low...they could bump their heads on it...
Also, if they are near it when it is closed, they could do some damage if they get pushy near by...
My new barn has a huge sliding galvanized steel door.... The horses are not near it but if they were, they would need some serious artillery to bother it,...lol