Why bother? If $50 changes your tax liability (it most likely won't) then it would only reduce it by $1 at the absolute most. But even so, no, your entry fee is not deductible unfortunately. However, if you won a prize in excess of the entry fee, then the amount in excess of the entry fee "may" be taxable income. It just depends on to many factors to list here.

Your $50 was not a charitable donation.  You got something in return--the chance to win a prize.  It is not deductible.

Thank you. I participate in many horse events for non-profit groups and had always wondered about this.

That's not to say that all charity events are non-deductible.  It's the prize aspect that makes this the equivalent of a nondeductible raffle.  If you have a riding event with no prize, where are you are paying for a dinner, or the use of a particular facility, then the value of the deduction is your donation minus the value of any tangible benefit you received.  For example, if you paid $50 for a charity dinner, and the fair market value of the dinner was $25, you could take a charitable deduction for the other $25.   (If the dinner includes a raffle, or a Chinese auction, the additional money you spent for that would not be deductible because of the gambling aspect.)