There may also be a difference between a horse drawn artillery piece with wooden or metal spoked wheels and metal "tires" and metal wheels with solid rubber tires and metal wheels with pneumatic tires in the speed you can tow them without shaking the gun apart.
I other words they may be a difference in "horse traction", "motor traction" and "high speed tow".
You are absolutely correct. Farm machinery is the closest example I can think of. A non-suspended solid-tired piece of machinery(a towed rotary bushhog is a great example) had a top speed on a paved road of about 15 mph. On an unpaved but maintained dirt road it drops to less than 10 mph without shaking the machine and the tractor both to death. Non-suspended pneumatic tired machinery(a large towed scraper) can be pulled pretty fast on a smooth paved surface, on a dirt road, speed is cut substantially,(down to about 15mph) again due to shaking the machinery to death. Suspended, pneumatic tired machinery has no speed limit except for rated limit of the tires.