Are you asking if the horse food for the client's horses can be written off?  Sure, why not if it is part of the business expense.   

Can you clarify what this means   health insurance that she uses to demonstrate the training with?      

Health insurance for the horse.

What category should I list the expenses under?

Normally, people pay to have a horse boarded and trained, and that fee includes food. Then, the facility has animal feed expense. Vet bills and shoeing are passed along and often with markup. The insurance paid for would be general insurance; the owners would have horses insured.

Are you sure this person even understands their own business model?

I think the OP is referring to the horse that person uses to make her training videos. Not the horses she boards or trains. She owns that one horse.

No their business is still in its infancy stage.

Yes I am referring to the horse she owns.

The horse is livestock as an Asset. It isn't an Expense.

And you can deduct insurance that covers your assets. She was asking about feed and insurance for the "asset"

Does she keep a log of business furlongs vs. personal furlongs?

Or if it's a gaurd horse it might be hours on duty vs. hours off duty.

I don’t understand your question. 

Are you asking if she keeps track of personal use versus business use?

I think Bob was trying to be funny asking if she's tracking mileage. 

BTW - I thought the horse expenses were for client's horses while there for training not a personal horse being used for business.

Yes.  And maybe for some history of this horse.  It's been in the family for a decade, she rides it every day and does videos every other Thursday?  When others see "horse," IRS sees "hobby." 

The client started off with her horses as a hobby but as she furthered her knowledge in natural horsemanship she decided to start a business as a trainer and decided to write a book. She also does a little boarding. Last year was her first year in business and she grossed $14,000 this year $44,000. The business is growing. With that said the horse she is using for business started as a personal horse.

I am picturing her business name on a magnetic sign for the saddle, so that she can claim 100% business use like the people who put magnetic signs on their cars. Do they make saddles that attract magnets? At some point, it may be reasonable to argue that there is a business purpose for her to have her own horse. The facts and circumstances so far haven’t convinced me, but you’re the one signing the return.

If I was preparing the return -  I'd allow feed and expenses for the horses she is training and boarding. 

For her own horse, I'd want to know how much time the horse is participating in business activities before I'd start deducting feed and expenses.  I would not treat the horse as a business asset for depreciation purposes.