I have a gelding that I raised. I was there when he was born. When his front feet emerged I immediately noticed he had one rather upright and one flat foot. The upright foot is not clubbed really but the flat foot is flat. BUT, he also does the grazing maneuvers that you describe, always places the flat foot forward. He has no trouble taking either lead and is extremely smooth, even though looking at his feet you would never guess it.
Lee ".......and God sought to bestow upon man a supreme mark of his blessing. God created the horse. The horse could run faster than the deer, jump higher than the goat, and endure longer than the wolf. Man, being encompassed by elements that sought to destroy him, would have been a slave, had the horse not made him king."