I'm not in on this one, but have some advise. I've gone cross country on a motorcycle before and have dealt with a few of the problems you will be having. For one I didn't have enough money to get hotels so I brought my tent. I hooked up with people I met on a motorcycle forum and whenever possible I crashed on their couch, washed a few clothes, thanked them and left. I'm sure people here would help you with that, it seems like a good group of people here. You will need at the very least to have contact info with horse people the whole way in case you or your horse needs medical attention. I can't remember the site but there's a GPS designed for hikers that you push a button and it calls 911 for you.
Also, you and your horse need to be conditioned for the trip. The way I conditioned myself for a motorcycle trip would be similer to what you will need to do. I packed the bike like I would be gone for a month, then rode to the lake about 2 hours away and camped. I brought a notebook and wrote what I brought and didn't use, brought and used, and what I wish I would have brought. Also logged how the load sat on the bike as far as weight and bulkyness. The next few trips varied from 2 days to 5 days out, logging the same way. I purposely rode in all types of weather to make sure I was bringing the right clothing for it. By the time I actually left there were no suprises and I brought just what I needed. I used a sport bike BTW, I didn't have any more storage than you will. The hardest thing I had was keeping the maintence up on the bike, much like you will have to keep up on your horse.
Sorry for the book, hope this helps though. If you make it through Ohio I have a 5 bedroom house and room for at least 5 or 6 more horses, you're welcome to it.