I see you are from Ohio, as I am too! It does get really cold here and we do get a lot of flies so fly masks are nice and maybe even a blanket even though I don't blanket my horse. You sound kind of inexperienced with horse, and if you are experienced I am extremely sorry, but I suggest getting some simple lessons on how to care for a horse. You can ride bareback. It's worse than riding with a well-fitted saddle because you don't distribute your weight but bareback won't hurt them really especially if you aren't overweight. I know that Bosal Hackamores are what a lot of natural horsemanship people buy, and that doesn't go in the horses mouth like a bit, it's just a special noseband that uses pressure points for controlling. Supposedly thats what the native americans used. If I were you, I would look for a horse from the ages 13-18 years old.
You will need halters, a nice fitting saddle, some first aid like vet wrap and ointment and telfa pads, a lead rope, treats :), and you obviously need food, pitch forks, wheel barrels, Bedding, grooming supplies (A body brush, face brush, curry comb, and a hoof pick will do just fine.) Please remember that you need to pay farrier every 6-8 weeks and you have to have money for accidents for the vet, etc. Also, If you are keeping the horses at your place, it would be a good idea to get a trailer in case of emergencies.
"If your horse says no, you either asked the wrong question, or asked the question wrong."