I used to ride a TWH and he was an ex-show horse, big pads, big lick. We rode him in many saddles, from western to jumping saddles. My Passier dressage saddle with a medium wide gullet fit him no problem, and all I used for padding was a thin line pad and a western saddle blanket. He had no pinching or dry spots.
With the few Walkers I've rode, and lessoned, on, I've noticed that their chests will widen with continuous work. Not as wide as a bull dog QH of course, but pretty buff compared to when they weren't being worked. And I rode Walkers that were used for beginner lessons, novice jumping and dressage lessons, as well as being retrained for Gaited Dressage. When they're ridden two times a day, six or seven days a week, they'll get a very nice chest to them.