We went for OH's 50th in mid February, we were not prepared for how incredibly cold it was, it snowed every day, in fact the airport was closed and we had to stay an extra night! It was hard work walking anywhere as the snow was knee deep, it was really windy and -20 a lot of the time.
We had a hire car booked, we cancelled it even though my OH is a confident driver. I really wouldn't drive the road signs are in icelandic outside of Rekjavik including the road closed ones, there were abandoned hire cars everywhere and the locals were telling us it was crazy to drive small cars there in winter!
The golden circle tour is great but v v busy, you find yourself with dozens of other bus tours spending 20 minutes at one of the wonders of the world, we found it all too rushed.
We went with a small independent company for a semi private tour, to the smaller waterfalls and a glacier walk, group of 8 of us with a young Norwegian guy and it was def the highlight if the holiday.
If you see the Northern lights consider it a BIG plus, it is not guaranteed at all, our hotel had a mini bus which went out to a dark spot every evening, saw nothing all week, the owner told us he has to manage expectations about them all the time.
Everything is eye wateringly expensive, we found a local supermarket in the end and had sandwiches on a couple of evenings after the £120 bills for basic evening meals we had paid (we don't drink!).
Would love to go back but wouldn't go in the winter it was too much hard work!