What exactly is covered in the price you're paying? If it only covers your percentage of the horse's board then you may be expected to pay something on top of that for farrier work, though generally speaking in a part lease the owner would have you pay one price that covers your portion of everything. For example, if board is $400/month and farrier is $100/month you'd write the owner a check for $250 to cover your half of costs rather than paying them individually for each item. In some part leases you're expected to cover a percentage of everything, while some owners are happy with you just covering a percentage of board. Either way, discuss with the horse's owner exactly what you're expected to pay and when you have access to the horse. What days you can/can't ride, whether or not you can ride off property, etc, when payments are due and how much, etc. Put all of it down in writing so there's no ambiguity- it protects you from the owner suddenly trying to dump the farrier bill on you, and it protects the owner from you saying you don't have to pay your portion of the bill.