You know what would be even more cool? Loosing the compass altogether and using the sun and shadows for orientation. But I'm not sure how it would work at night. Are the stars a trustworthy guide for direction?
I though on that at start, and even tried to learn about the moons and some mountains to try doing it, before disabling the compass. Noticed that a moon was always East, and that 3 stars where at another direction.. the problem was daylight, cloudy days, or snow storms.. so as it was too hardcoe for me, I decided to leave it for a second char, once I knew the gameworld better. After 450 hours I started it, but to be honest I'm still with my compass around. I can survive without quest, locations, and enemy markers, but without compass I'm doomed.. if I exit a dungeon from a backdoor, I know more or less where I am looking at the paper map, so I know for example Solitude is northeast, and I try finding my way there... without it I could walk south and don't notice it until I get to a familiar area.. Which could be cool sometimes, but not always.. walking 40 minutes (I don't run) to find out you just headed the opposite way, its frustrating.
Anyway, tell you something.. maybe I try it.. it could add a bit more immersion and realism.