I am an equestrian.

The actual type of bit is a loose ring snaffle if you need it to be exact.
would love to help if you have more horsey vocab!

--------------------------------------------------
Note added at 31 mins (2011-02-23 16:14:47 GMT)
--------------------------------------------------

this is a great website:

http://www.equisearch.com/tack_apparel/bit_gallery

--------------------------------------------------
Note added at 49 mins (2011-02-23 16:33:04 GMT)
--------------------------------------------------

hi guys, yes sorry, was rushing in my excitement (sadly!) wasn't paying attention!
OK, so yes mouthpiece is used, but also the same word "cannon" in english. ALSO in North America, that part of the bit is called the bar.

e.g.
B is called the cannon if the bit is jointed, as this one is in the middle. The cannon is the portion between the rings and the middle joint. The cannons can come in many shapes and widths. They can be very thick and tapering to the middle, or they can be very thin, as with a bridoon, meant to be used with a full (or double) bridle when the horse carries both a curb and a snaffle bit at the same time. The cannons can also be twisted, either solid or of twisted wire. These variations make the snaffle bit more severe.

this from : http://horses.about.com/od/bitsexplained/ss/partsthesnaffle_...