The snaps are said to irritate the horse as they will have a bit of friction when they move that is metal on metal and that vibration can realliy be felt through the metal bit, on top of whatever clanking souund the human rider can hear.
The purpose for the slobber straps (is that a weird name, or what?) is to transmit the change in "weight" of the rein very immediately to the bit. The straps and the rein have weight such that when they are hanging (loose rein) they have a feel to the bit, when the rider picks up one rein, some of the hanging weight is diminished. AND, as the rein is lifted the slobber strap changes the angle it has to the bit as it slides on the loose ring of the bit. The resistance of the leather on the bit (especially if the slobber strap has some real width to it) can be felt by the horse really quickly, so the horse gets the message coming through the rein before there is any real pull on the rein , just by the feel of the slobber strap itself.
If I was doing a lot of trail riding, I might do the metal snaps because there are times when it is good to be able to detache ones reins quickly. If I wanted to ride western and do training, I would do rope reins with slobber straps.
They can be ordered online from many sources.
Any good, heavy leather would work for making them.