I have a Jerald runabout cart. I've used a 29"-35" horse with it. What is the tallest horse that would work in my cart? With the tug straps on lowest hole, the shafts were nice and horizontal on the 35" horse.
A lot depends on their build. I have had a 39" horse in mine but he is slender and short bodied. They need to not only fit the shafts heightwise which as you mentioned can be adjusted for by the length of your tug straps and if necessary you could even get larger wheels for it as long as your horse fits the shafts.