Could be, is he lame on the flat/a circle? Could be weakness as far as muscles are concerned too, my girl tripped over fresh air when I got her and it was just down to lack of muscle :s
Maybe not necessarily, though may depend on the circumstances. From personal experience i know that my share horse used to stumble down hill as a youngster as he was not using his hindquarters enough, as he has grown up and got fitter he does not do it now.
Yes my horse used to stumble going down hill when I first got him. He was unfit, with poor muscle tone and unevenly shod. My farrier spent a long time rebalancing his feet.
So, poor shoeing could be a factor for you?
We have a 15 yo on our yard which makes a real 'meal' out of going down hill. He swings his front legs out in a strange way and would probably stumble if we didn't hold him together. Turns out this is a classic symptom of arthritic changes in the hocks according to our vet.