Foaming in the mouth is not due to strenuous anything, and even lower level horses will foam at the mouth.
There should not however be an excess of foam, we want it like lipstick. I'm going to steal Duffy's photo because it illustrates the kind of foam we want!
There can even be more and it is correct, as long as there is not foam flying everywhere!
Basically it shows that the horse has a relaxed jaw and is working into the contact. There should always be a pressure in the reins that is not from the rider pulling, but from the horse stretching into the bit to raise the base of his neck and round from the withers to the poll equally. This of course is caused by the motor behind propelling the horse into a soft contact. But the end result is having a soft jaw and a foamy mouth.
Dry mouths are the result of pulling, or a horse who is not suppled or working into a contact. Most horses ridden without contact will not foam. Horses on a contact that are not foaming are being ridden with hard hands and are hard in the mouth. They are being ridden front to back, with too much hand.
I hope that makes sense!!
The soft jaw allows for increased salivation and as the horse softly chews and moves the bit, air enters into the saliva and foams.