1

If weather is good, and your gear is good, then it should be Ok.
But if weather is not good, and you equipment is not good, I wouldn´t recommend it.
What kind of a question is this any how ?!

2

In January & February? No, no, really no! The weather is definitely not suitable for camping unless you're a serious hardcore winter camper and have all of the right kit for camping in cold, snow & strong winds. Not to mention the fact that days are short and nights very long at this time of year.

3

I once read a funny story about the police finding a couple of people with bicycles camping in a tent in a blizzard, near the road a long way from habitation in SE Iceland one Feb, and trying to rescue them. They resisted being rescued on the grounds that they weren't in any difficulties, and had made arrangements for camping in such conditions, and their present location was consistent with their plan. They had special trailers that converted to sledges that enabled them to haul their bicycles over snow-covered land, and had just crossed the centre of the island, so in fact being by the ring road was a picnic in comparison to their recent locations.

The difficulties you will suffer include the fact that weather ranges from snow to rain, the ground conditions vary from snow lying, to snow melting, to no snow and mud. And although many villages have small, often free, campsites, with a toilet block, they will often turn the water off and lock the door in the winter, to protect against frozen pipes and wind damage. They also have some serious winter storms from time to time that would require you to have an expedition quality tent, and given the range of ground conditions a lot of tent pegs of varying types - I take two kinds of tent peg just for summer camping in Iceland as the ground conditions are so variable.

So if you are a conditioned winter or high altitude mountaineer used to camping around and above the snowline, and weathering mountain storms, it will all be in a day's work for you. Otherwise you are going to be somewhere in the range from very uncomfortable to needing to be rescued.