This is just me, but personally I wouldn't spend much time on writing the notice. I'd write up something simple like "This is my notice that on DATE I will be moving my horse, NAME, from STABLE. I have enjoyed my time here." Then I would sign and date it (make sure there is a current date on the notice, in case anyone later tries to say it was less than 30 days).
Then I would go to the trainer and talk to her, explain my decision, and then just hand over the notice calling it a formality. I wouldn't be using the written notice to explain why I'm leaving - I do that first, and use the written notice just so the legal requirements are met.
Of course, some people prefer to do it the opposite way. If you think it would be too difficult to have that conversation, then you can write out a detailed notice. However, I've found that most people don't want to read much - they prefer talking about it. I ALWAYS write formal notes (work emails, official notices) with the assumption that the person will not read more than the first sentence. So that one sentence has to say the critical items in a short, concise manner, and the rest of the message is to back it up.