[QUOTE=flyracing;8938592]
You’ve probably seen the scenarios of a leather strap on a snaffle a lot then and just haven’t noticed. Its very common. Here is a picture of how a chin strap is used on a snaffle: http://www.chris-cox.com/tack/bits-1
I have no idea why, so don’t ask me 
Taking the curb chain off the curb just takes away the leverage affect and I’ve seen it done when the horse doesn’t have a snaffle bridle but the they are letting a beginner ride. You won’t see it in a show or other formal situation![/QUOTE]
[QUOTE=SendenHorse;8938753]Did you mean to ask people who have actually seen this?
I don’t know, it makes more sense to use those or a full cheek. I really can’t understand why people would tie down a snaffle. it totally changes the feel and dynamics.
Honest thought- for anyone, if you are actually worried about pulling the bit through the mouth, maybe there is a deeper problem? :)[/QUOTE]
There is definitely just a “fashion” aspect about it. However, a snaffle on a western horse is still used with a looser rein. Also, western bits are often left lower in the horse’s mouth so the horse has to use its tongue to hold the bit up - tongues sticking out run in multiple lines, and it can help keep the tongue in the mouth while riding. (I’m not talking tongues out in protest - my last QH had Skipper W lines which were attributed to his tongue being constantly out when standing around with no bridle, except when riding him when he’d put it back in his mouth.) Anyway, if the horse is moving the bit due to that or just correctly softly chewing, and the headstall is looser and reins are loose - the bit rings can flop outward instead of looking steady and pleasant. A leather curb strap can quietly hold the rings in the correct position - not holding them clamped, just loosely keeping them from flipping out - it’s really irritating when you’re riding a more trained horse and the bit flips over due to tongue use on the part of a horse, but on a young, green horse it could be dangerous. I’ve seen multiple horses do it while standing around.
Mostly, though, it’s the “fashion” and done without much thought…