the most common tack

Icelandic horses are usually ridden with tack designed specially for the breed. 

The most common tack used consists of a simple bridle with a regular snaffle bit, either dropped noseband or an English version, and Icelandic saddle (rather similar to dressage saddles) and sometimes a dressage type whip as well.

The rider typically wears riding pants, often jodphur trousers with riding shoes or boots, any type of comfortable jacket or sweater and a proper riding helmet.

Do you need tack or other equipment? See list of companies below:

Lýsi 
Lífland
Hrímnir