It's not clear what you mean by "the boarding." You can deduct your actual out-of-pocket expenses for things like food and veterinary care that are not reimbursed by the organization. I doubt that you could deduct anything for stable space, for example, because you have no direct out-of-pocket expense and you are not turning over ownership of the stable to the organization. You cannot claim a deduction for donating the use of something that you continue to own. And you certainly cannot deduct the value of your time.
You have to keep good records of the expenses. The article that TaxPro+40 referenced discusses keeping records.
Also note that donations to a charitable organization are an itemized deduction. It will not make any difference in your taxes unless your total itemized deductions are higher than your standard deduction. The standard deduction this year (2018) is much higher than in previous years, so most people will not have itemized deductions that are more than their standard deduction.
