It does need a process with a clear understanding so that both you and the owner understand what it will be.
“of course if something comes up, you can get out of the lease.”
Does that mean to her that if I call her and leave a message on her voicemail on Sunday May 31 that I’m not going to ride any more that we’re all good that there will be no June 1 check? Does it mean if I text her on June 10 that I’m done that she refunds 2/3 of my June payment? My guess is she’d be mad in either of those cases.
She may be thinking that you’d ‘work it out’ when the time comes. That’s not the best plan. Clear expectations are the best plan. You or she are always welcome to informally renegotiate if something unexpected happens; she can always be more generous if circumstances permit, as can you.
I think what’s fair and reasonable and simple is that either party can cancel the lease for any reason or no reason with 30 days written notice. She as the owner will always have 30 days to replace that income or find a new rider for the horse if needed; you as rider will always have 30 days to make other riding arrangements. You as rider never have more than 30 days’ liability for the bills; she as owner never has to put up with more than 30 days of your annoying or irresponsible conduct. 
You can try to write something more messy to include unforeseen calamity, but I think the simple 30 days is a better place to start. It protects you both without requiring someone else to adjudicate fault, blame, soundness, fitness for purpose, etc.