In reply to Tim Chappell:
Iceland is fantastic in the winter and there are far fewer tourists about.
We spent a week driving in Iceland last February and had no real problems and we covered over 2000km. Your rental car will come with snow tyres fitted which help enormously. The main thing to do is to remember to stick to the main roads and not to be chicken about driving on frozen/snowy surfaces. The F-roads are off limits at that time of year, anyway. Your main issues are strong winds, snow, ice and sandstorms especially when crossing sandurs.
There's an excellent Icelandic road website that gives you all the info in english.
http://www.vegagerdin.is/english/road-conditions-and-weather/
Our longest journey in one day was just over 800km from Reykjavik to Jokullsarlon. Things got "interesting" at Vik when the road was alternatively sheet ice or covered in blown snow and we were glad to see the snow plough but it was fine.
Don't feel inhibited, plenty of people will be out doing the same.