It's incredibly common.
It's not the clover that causes the drooling, it's a fungus present on the clover at certain times of year. I'm in central Virginia and my pastures are full of both red and white clover and the horses drool like crazy. There are actually wet patches in the barn aisle in front of their stalls.
It is not harmful, and the clover is not toxic. As a matter of fact, since clover is a legume and not a grass, it's a very nutrient rich food. The risk from having horses have too much is founder! There's no other inherent problem in clover as a food that I'm aware of. I find it entirely credible that a horse on good pasture in Maryland at this time of year has the clover slobbers, as it usually called around her.
I've never heard of drooling as a symptom of being doped, but it that's a concern, have blood work drawn as part of the pre-purchase.