Put the harness on her, run the traces out behind. Have a second person to help you. Get something like a stick or rod of metal, to run the traces back and attach to. One person holds the stick or rod with traces pulled back like she was hitched. Other person goes up beside horse, moves the traces wider so they are not touching her sides. You then mark the stick or rod with both places traces are located and not rubbing her sides. That will give you a measurement for the width.
I am betting her sides are wider than her hindquarters, from viewing the photo. You want the singletree wide enough to prevent any rubbing her sides as horse goes ahead.
Where in Michigan are you located? With the Indiana Amish so close, most folks buy a lot from them for Draft horses, pieces/parts needed for vehicles and pulling. There are also Michigan Amish groups up past the midway point in the middle of the State, that might be closer to get help from.
You may want a steel singletree for pulling logs, less chance to get broken or wet in our weather, plus handle the weight of logs.