The tack used for Icelandic horses is slightly different then the tack ordinarily used for other breeds. The saddle is built close to a dressage saddle and has a relatively flat seat. Saddles come with plain or quilted seats. On longer rides a crupper helps keeping the saddle in place. Riding style used on Icelandic horses is close to English riding style, but stirrups are worn long.
If you are riding the Icelandic horse it is recommended to use an Icelandic saddle, made especially for the Icelandic horse. The main reason is, that they put the weight of the rider too much forward. The rider is thus resting it´s weight on top of the withers of the horse, or very close to it. Sometimes even interfering with the movement of the shoulder blades. When the horse lifts it´s leg and takes a step in tolt, there is a huge rotation happening in the shoulder blade, and the horse should not have to squeeze the shoulder blades under the saddle in every step. To get the Icelandic horse to free it´s withers, riders have to be resting their weight a bit more behind on the horse than on many other breeds, endurance, dressage, western and other such saddles.
The tree, and consequently the panels of the Icelandic saddle are generally more flexible than traditional English and endurance models. That helps the horse free the shoulder, it improves saddle fitting and makes it less likely that the horse gets sore from the saddle. Not all saddles made for Icelandic horses are great, and some saddles made for other breeds work superbly for the horses and their gaits, but this should be given a thought before selecting a saddle for the horse. Few questions riders also need to take into consideration: How is the saddle fitting the horse? Does it poke it somewhere? Does it give the shoulder blades enough space to rotate? Is it helping centering your center of weight over the center of weight of the horse?
It seems as though the position of the stirrup leather on an Icelandic saddle is further back and straighter down than more typical English or endurance models. This keeps the leg more towards the middle of the horse and also away from the sides of the horse.
Bits used are mostly simple snaffles or Icelandic curb bits. Bridles have a detachable nose band and clip on reins.