You are right...a saddle that does not fit right CAN effect a horses way of
going. If it opinches his shoulders, he won't want to move his front legs
forward, hence tripping.
I had a horse that was lame when I rode him and fine at the vet checks when I
trotted him out...drove me crazy (and the vets thought I was crazy). Turned
out he had one leg shjorter than the other, hence his shoulders did not match
and the weight of the rider caused the saddle to restrict that
shoulder...hence he was lame. A great farrier and good shoes and foot length
solved the problem very quickly (after 6 months of frustration).
Teddy