All of my horses ride wonderfully in snaffles, even my Bosal horses occasionally.
First there are misconceptions with bits in general;
Snaffle- Any bit that does not have leverage. Can be straight,1 joint,2 joints,"waterford" 5 joints. Multiple mouthpiece materials-Plastic,rubber,copper,stainless,sweet iron,etc...
Curb-Any bit that does have leverage, Same as above with joints,materials. The side bar severity depends on its length and type of curb[part that goes under chin.]
Gag- Its effect on the head, combination of mouth,chin and poll pressure. Again comes in many mouth pieces and materials. When reins are pulled it either slides on cheek pieces or twists to pull pressure on poll.
Hackamore- Does not have a mouth piece.
Combination-Has both a mouth piece and a nose/chin device.
All of the mouth piece bits can be of any material and feel. Can be smooth or twisted, triangle shaped, balls or rollers in center, bendable or hard. The sides also are different shapes for different functions.
The exact same mouthpiece can be in each bit, for instance;
A jointed mouth piece with a "D" end is a D-ring snaffle.=Snaffle
A jointed mouth piece with a 2" shank end a Tom Thumb.=Curb
A jointed mouth piece with a sliding cheek piece a Gag.=Gag
A jointed mouth piece with a rope nose and a shank end a Reinsman stop and turn.=Combination
So a "snaffle" is a type of bit, from there you have alot of choices. Its like saying I drive a "Ford" the possibilities are endless.
You may have to do a little research, Myler explains some of it but any google search should work.
The milder the bit the better trained your horse is, so be patient and go slow. You should never be in a hurry and certainly don't try to use strength or force.
I own 64 bits all different and probly use 25 pretty regular, but of those only 3 aren't snaffles.