The Icelandic Road and Coastal Administration monitors driving conditions all over Iceland. In the winter time their web is our number ONE. There you can see maps of roads with info on the temperature, driving conditions and how many have been going that way in the last 10 minutes. There are also webcams on many of the most travelled roads. Special warnings are issued when very bad weather is on its way.

Their website is www.road.is
From their site:
The best way to get information about road conditions and the weather on the road system is to call 1777 (if problems use +354 522 1100,   +354 522 1100). Open 8-16 in summer and 6:30-22 in winter. An English answering machine with similar road information is in phone number 1778.