WOOOOOO KESMARC!!!!!!!!
I formally interned there (the Kentucky facility) two years ago, and I've returned nearly every Thanksgiving, Christmas, and Spring break since I live nearby. My internship was 100% the best summer of my life: I worked with some incredible horses, made amazing friends, had the opportunity to participate in fantastic medicine, and made alot of professional connections.
That said, I'd never worked with horses before, so alot of the joy was likely the result of novelty
The work is variable -- some days you'll just be doing alot of bandaging and medicating, others you'll have a vet show up to collect stem cells, one to do lameness exams on a dozen horses, and a third to scope yearlings going to sale.
Lots of students generally intern over the summer, so you'll probably have a fun group of people to work with.
As to getting your letter, it depends. You'll have the opportunity to work with alot of different vets, but there's no single supervising DVM. You can probably arrange to go observe surgeries at Woodford equine if you can be spared from the barn, and you can find a vet to ride with on your day off. I think obtaining a letter would be doable if you were focused on it, especially if you talked to Lanie beforehand.
Please PM me if you want to talk more!
ETA: the work description posted by thelarson above is pretty accurate in my experience. And I didn't stay there, but I will say that the apartment kind of sucks