Actually, rule 918 section 1.3 states if the vehicle does not have brakes then breeching is required as a part of the harness. Most people continue to use breeching for the marathon even if they have brakes on the vehicle.
I have seen many different types of vehicles used in CDE. If you currently own some type of cart that is safe then it probably ok to use at an event at least at training level. I used the same harness I had for the show ring my first two events. Just make sure it fits the horse correctly. I was able to add the breeching at very little cost. ( None of my carts had brakes)
I hope you do find a venue to become involved in the world of combined driving. It is best if you could find someone that has been competing for awhile to mentor you. You may want to support the organization that provides the officials and rules for the events.
Ron