You may not have heard that in Iceland we have not only 1 Santa but 13 santas or Jule-lads.
These Jule-lads live in the mountains with their troll of a mother (Grýla). Thirteen days before Christmas they start showing up amongst the people one by one.
Nowadays they give small gifts to good children in a shoe that the children put in their window each night. But traditionally they were mischievous and each one of them has his own characteristics.
The first to arrive on the morning of the 12th of December is called Stekkjastaur, he can be recognized by his stiff legs. His characteristic is that he loves to play pranks on sheep wherever he can find them.
The second arrives on the morning of the 13th. His name is Giljagaur and has gray hair. His main characteristic is that he goes into the cows stables to steal the fresh milk.
For more information on the other Jule-lads and other christmas traditions in Iceland check out this site for the days until Christmas.