While many people do make the drive in the winter, I wouldn't personally recommend it for someone who has never done it before and/or isn't familiar with winter driving.

The railroad is a wonderful way to travel, but as vysean alluded to, you won't see much in December due to the lack of daylight.

AS just announced a sale which has $79 ow flights between ANC and FAI. You might want to look at that option.