I have heard that peppermints can cause a horse to test positive (for something?) when drug tested at shows. I asked the show vet and was told that peppermints CAN test but only when given in very large amounts. For whatever that's worth--and slightly off the subject.
The conventional wisdom on peppermint oil is a very mixed bag. It is often used for dyspepsia (sour stomach, etc.) with much anecdotal success, but the fact remains that it can decrease the tone of the lower esophageal sphincter, thereby theoretically worsening reflux.
Since not everyone with dyspepsia has actual, anatomical reflux, it'seasy to see how confusing this is--most of the terms we use for general GI symptoms are not exactly anatomically correct.
I always thought you grabbed a mint in the restaurant because you'd eaten too much yummy, garlicky, oniony, olive-oil laden Italian food.
I wouldn't bother giving them at all, because there are better, nicer things for a horse - all the human fruity cereal products spring to mind - I'm on Kashi Berry Blossoms at the moment I worry about the sugar content in mints for ulcer ponies, and if there's no sugar, I worry about the nasty sugar alternatives like aspartame that give me instant headaches and runny tummy - I definitely won't be giving those to ulcer-pony !
This was what my vet told me while I when I was treating a horse for SEVERE (god her stomach looks like the Jersey Shore) ulcers.
Peppermint oil itself is not bad for the stomach. The problem is in the sugar the mints are laced with. Sugars (like molasses in sweet feed) lowers the ph of the stomach causing an irritation to the ulcers itself (thing of pouring acid on an open would).
That said, two mints won't kill them, but while I had a confirmed case of ulcers that I was treating, the mints came after the ride along with some alfalfa cubes to combat the PH lowering. If you are looking for something before or during a ride, try mint flavored tums, which will also help to raise the PH in the stomach, therefore making the ride more comfortable as the horse is moving and its stomach contents are sloshing around as well...
Sugar cannot lower stomach pH as its own pH is MUCH higher than that of the stomach. A diet high in sugars can impact HINDGUT pH, perhaps, but would have no impact whatsoever on stomach pH, which is down around 2-3 all by itself. Kind of hard to make it any lower, short of feeding the beasts pure hydrochloric acid.