OP… Be sure the hitch coupler fits the ball, and that neither are worn. Hills and turns put a lot of torque/stress on that connection.
Do give plenty of thought to the length of your trailer+vehicle and how sharp the turns, and how steep the hills, are.
You don’t want to jack-knife the rig, or have to play crack the whip, making a hairpin turn. You don’t want to go into the on-coming lane to keep your trailer from cheating to far to the inside on of turn.
Think about entering your driveway from the road, and pulling out onto the road from the driveway. Do you have a wide enough culvert?
I find on twisty turning roads if you are able to go slow the horses can stand up on their own. If you have to maintain a quicker minimum speed, many horses like to lean on a support.
In the winter, a stock trailer is draftier, but it’s airier in summer.