In bold if from the American Driving Society website.
One of the first questions people ask when they go out looking for a carriage is "How do I know if it will fit?" Over the years there have been several charts printed to aid people by giving dimensions to help in buying the right size. This is a compilation of some of that information into one chart. How is this kind of chart possible? While horses body types are not identical, there is a dimensional ratio between various parts of the body compared with the height at the withers and this is adequately similar for the purposes of shaft design for different sizes of horse or pony.
What parts of the body need to be considered? Wither height, width at the shoulder, width at the saddle girth, croup width, length of trunk from point of shoulder to buttock and location of the stifle. An additional consideration is normal length of stride. Taking all these factors together helps define the space needed to give the horse sufficient room to move and to be comfortable, while also allowing room for the harness, and some leeway for a slightly larger or smaller animal. The information in this chart defines approximate dimensions needed to build or buy a traditional style of two-wheeled single horse vehicles or 4-wheeled pole type vehicles to fit a wide range of horse sizes. Adjustments may need to be made to accommodate heavy draft type horses, donkeys and small ponies or mini-horses. Vehicles designed for specific purposes like the modern marathon vehicle or an antique gig will often differ in dimensions to meet their specific needs. For example: marathon shafts are shorter and end at the saddle girth, or some gigs are made with narrower widths between the shafts. The size and design of the harness may also affect how a vehicle fits. A bulky saddle could require more space between the shafts. Style of breeching may affect the position of the breeching staple. Also the chart describes wheel height for two-wheeled vehicles. Wheels will be smaller on four-wheeled vehicles.
Ok you now have some measurements of your horse, where the tug stops are hand its' height. Now what about the cart.
After measuring the cart and checking if the measurements are somewhat close to the American Driving Society's chart above, for your horse.
For example if I have a 15.2 hand horse I would look for a cart that has these measurements:
Length of shaft from single tree to tip: 75 - 80"
Height from ground under shafts at back band tugs: 49 - 52"
Width between shafts at back band tugs: 23 - 24"
Width of single tree 31 - 34"
(I like measuring the width between the shafts at the cross bar)
Length of back band tug to shaft tip: 20.5 - 22"
Length of back band tug stop to trace hook: 50 - 53 (singletree hook)
a lot of carts don't have tug stops, you can use the measurement from the tug to the singletree hook.
Distance from breeching staple to trace hook: 27.5 - 29"
(holdback irons to singletree hook) (these irons can be moved)
Wheels diameter: 45 - 48"
Again this is just a guide, I like to err on the large side, especially in the width between shafts and singletree size. I have big horses though.