Four horned Icelandic sheep: rarest of the rare
There is not a lot known about the genetics of four horns, but I will share here some of what has been written. Dr. Olafur Dyrmundsson of The Farmer's Association of Iceland wrote in a letter to the editor of the ISBONA Newsletter (Volume 5, Issue 1, Winter 2001) the following comments:

"...from my point of view we have the duty to preserve rare genetic characteristics such as 4-hornedness in sheep. Fortunately, quite a few are still found in Iceland. A few individuals, mainly colored, are found in some flocks, and I know one farmer who has been concentrating on the breeding of 4-horned sheep for nearly 50 years. Most of them are brown-piebald (moorit spotted). There was a 4-horned ram in the AI services several years ago and it may be tmely to offer such possibilities in the near future."

In an email correspondence with Dr. Dyrmundsson he wrote me:
"..there are some genes for 4-hornedness around out there. It is a primitive trait. We don't know much about the genetics of this trait, it can come from one parent, it is also found in females and is thus not linked to sex and not to color. Polled sheep may also carry the gene or genes for 4-hornedness..."
The photo above is of a 4-horned ram that resides in a park/zoo in Reykjavik, Iceland. Photo courtesy of Shawn Carlson.
Some of the Icelandic sheep breeders in North America had been led to believe (myself included) that we had sheep that were four horned. Occasionally rams are born that have small 3rd and/or 4th "horns" that grow from the base of their horns (see photo above). Dr. Dyrmundsson has recently clarified that these are not true multiple horns, but rather miniature "off-shoots." Dr. Dyrmundsson reports that true 4 horned sheep or polled sheep carrying the genetics for 4 horns, have heads that are much "higher." He also reports that the district in Iceland (Oraefi) from which the original importations were made into North America did not have any 4 horned Icelandic sheep.
Photo courtesy of Brynhildur Inga Einarsdottir