I'd say its a myth...
For example, if a horse has sand colic, turpentine won't get rid of the sand...
Or if the problem is a twisted bowel, is the turpentine going to fix that? I very much doubt it!
The thing I'm getting at here is that colic always has a cause and holding a tablespoon of turpentine under a horse's belly button cannot fix the cause! WIthout resolving the cause, the colic remains!
Additionally even if turpentine does has some medicinal value, I just can't see how the turpentine can affect the horse when its outside them - its vapour cannot pass through the skin and affect the horse's insides. Skin is impermeable to most substances - its how the body protects itself from infections.
It seems like a rather strange myth. Can you tell us where your husband heard this? I'd be interested to know
When I bestride him, I soar, I am a hawk: he trots the air; the earth sings when he touches it; the basest horn of his hoof is more musical than the pipe of Hermes. ~William Shakespeare