I own three TWH's -- three very distinct personalities, three very different sized motors.
The little guy (14.3H which is SMALL for a TWH) has a Rodak for a motor. He's the horse in my avatar and was 16 when that was taken on an organized ride lunch break. Looks wore out doesn't he? Not
I have trail ridden him in each of the states we have lived in. He never slowed down until he became sick with Equine Metabolic Syndrome two years ago at age 19-1/2.
When he was 15, he outpaced both my neighbor's younger Quarter Horses in a 36 mile round-trip ride in the low dessert of Southern California.
We had all spent an entire summer getting our horses conditioned for that ride. Each horse was in the peak of condition, yet their horses could not keep up with his non-stop gait and finally told me to just head on home without having to keep stopping for them. Headed home being the operative here ---- big heart & big motor.
I've owned this horse since he was coming 3. Always, when we would first start out on organized rides, I had better be willing to stay up front most of the day because that was where he wanted to be. Since he always finished a day ride coming back to camp in the top ten, I let him stay at the front of the pack.
He still has that huge heart and huge motor but his diabetes interferes with him going at high RPM's for too long these days.
It took me about the first five rides when I bought Duke to figure out Duke did NOT want to slow down until we were a half hour or so into the ride.
Well alrighty then, have at it big guy. He was happy at not having to keep trying to tug the reins away from me, I was happy he was happy at being allowed to move at his own speed while still being polite and respectful, and by the lunch break I was riding him on such a loose rein that even the Quarter Horse folks were envious
The BEST all around, most even tempered, never refuse to do anything Walker I own is that little guy with the huge motor. He's done everything from cold-stare down a tissed off male llama at two feet away, to flipping his ear off at some moron who let off his jake brake right beside us on the state highway. His most favorite thing in this life is to get costumed up and go in parades. I don't even cue him in a parade --- he quickly learned to start and stop himself according to the float in front him.
I know the "new way" of training is to round pen a horse and teach them respect before getting on them to ride. I have been riding 60 of my 62 years and never have liked tight constraints for myself. I am also from the old school where lunging for half hour in a roundpen (only people out west had those in the old days) before riding doesn't make sense to a mule, unless we're talking show horses. Just get on the horse and let it ride itself down --- which it will in due time.
I said all that to make the point that the horse in question here, while very gentle and mentally laid back, may just be a horse that likes to go-go-go and may be fighting being made to slow down until he's ready to slow down.
The horse you bought also may be cued a lot different than what you are used to and is reacting to getting mixed signals. My thought would be to talk to the previous owner, if possible, or hunt down some very experienced, long-time owners of Walking Horses, or buy a Liz Graves video. They don't get any better than Liz Graves when it comes to Walking Horses