As was already said, more than keeping the horse from overheating, trace clips were to keep the horse from cooling off WET. Have you ever washed your hair then gone out into freezing weather until your hair dried? The water would freeze before it would dry causing your horse to risk hypothermia. Short hair dries quicker.
The horse still has hairy legs, the top of the neck and topline of thehaunch are also hairy. Most of the clipped area is under a blanket in cold weather. Because the jugular notch is often clipped, they still need shelter in very cold weather.
I'm wondering how the poor horse regulates his temperature when he's clipped. Part of his body is ok and the clipped part is cold. It's ok for a horse to sweat into a heavy coat but most owners don't want the extra work of helping the horse dry out.
It would take hourse for a thick coat to dry. I have seen horse shiver while drying risking hypothermia. It is just not practical or kind to the horse to risk this.
A wool cooler wicks moisture away and walking helps the horse dry from the skin outward as does some intermittant munching on hay.
Again, it takes hours for a wet thick coat to dry.
A horse has the abilty to raise and lower his hair, plus turn it to catch cooling breezes or fluff it up to hold warm air.
The hair does not have the ability to "fluff" when it is wet. It plasters down and offers NO thermal protection.
Clipping takes this all away
No. Clipping gives you shorter hair that dries quickly, keeping the horse from losing too much heat through convective cooling. It helps protect your horse from hypothermia.
No one says that you have to clip your horse. You simply must scale back your riding or put your horse at risk. Not something that many of us want to do.