OK, these are just my THOUGHTS, because I have no experience with this, but plenty of experience with contracts, which is what you will want to create. (I am not an attorney either, this is just my 2 cents...)
1. Figure out what each of you wants to get from the deal and if money is one of the things (maybe it isn't). Hash this out at length. Every deal is likely to be different depending on what each person wants.
2. Talk over who would make decisions, how expenses would be shared (expected and unexpected - see below), how winnings would be split, and who decides what shows and classes, etc. How long will the agreement last? Where will the horse be kept?
3. Consider EVERYTHING that can go wrong - people and/or horses dying, getting sick (or laid off), being unable to show, etc. and figure out how each of these would be handled. Insurance???
4. Put everything in writing and run it by an attorney before you both sign it and initial every page (and any changes). If you don't want to spend money on an attorney to do this, think long and hard about what each of you has to lose in this deal.
Hope this helps, and good luck!