The second article that you posted first states: "How to tell that your horse is approaching his limitations:
1. Panting or blowing respirations
2. Heart rate more than 150 bpm
3. Profuse sweating"
It does not say Profuse sweating alone is a sign the horse is over worked. "To avoid over-working your horse in excessive heat, try to ride before or after the hottest parts of the day. Examine your local weather report to plan any lessons or strenuous riders during the coolest part of the week. Be prepared to spend more time after the ride to cool your horse off, which may include bathing or sponging with water, handwalking/grazing and monitoring your horse until his or her heart rate is back to normal."
This article just says to be prepared to cool your horse off differently, like a good hosing... it does NOT say that foaming is abuse. While it does say excessive foaming is a sign the horse is approaching its limits... however that is common in training, knowing when to quit but asking more of the horse then the week or month before.
BOTH articles seem to stress the importance of cooling out.
I think most people that have horses that get hot and foamy in the summer spend a good deal of time ending in the walk then hose the critter down before putting them up.
It seems by those articles, if your horse is worked hard enough to develop a lather proper cooling and hydration are the concern.
Again, neither article said foaming/lather is abusive.
But, I'm done talking about sweat. After working one up with my horse (yeah, he was a little hot today) and a good bath for both of us I'm callin it a day.