You won't have any trouble with either Hwy 1 or 101 as far as ice or snow. You could catch some rain in January so be prepared for that.
If for some reason you decided to go up I-5, there is a pass near the small town of Gorman that is a little over 4,000 feet. Occasionally a winter storm will drop snow up there, and the highway will actually be closed, though usually for not more than several hours. Just watch the weather reports.
The California Department of Transportation maintains a website
where you can enter highway numbers, ie "1", "101" or "5" and it returns current road conditions including closures: