Have a look at the weather site for Iceland. pretty detailed. What it can't tell you is how you will feel at particular temperatures. Have you been in cold places before?
I've been in March and May and it was about the same as the UK (March) as was May (same as UK in March).
I would dress as if you were ski-ing: thermal underwear; mid-layer, then outer wind/waterproof fleece layer. If it is windy then the cold will be worse. Hats and gloves too, obviously. Footwear - something to keep you warm and dry. Walking boots or shoes would do.
Reykjaviks on the coast so shouldn't get as cold as the interior, but will get the Atlantics gales that blow through in the winter. Or, you could get a high-pressure system which gives calm clear weather.
Having been to Reykjavik a number of times in December, I can say that you never know what to expect.
Snow in normally not that much of a problem, as a very significant accumulation is not that usual in Reykjavik.
The biggest winter problem is wind/rain-sleet. With temps in the low 30's (F), but with winds gusting up to 50mph for hours, it can be miserable to be outside for anything more than a few moments.
They really do have 'horizantal" rain there, as the winds can be so strong.
Have a look at this site:
It gives the hour by hour report for the domestic airport in Reykjavik for Dec 4, 2005.....but you can change the date. Look at the temps, winds, and precip for a number of days in Dec, 2005 and you will get an idea of what to expect.
As you will see, some days are fine but some can be brutal with the wind/rain.
i was in iceland in november and in february.
I found it was cold but not too bad. The rain made it feel much worse than it was, i think. It snowed when I was there in Feb but no snow in the city of Reykjavik, it was only rain.
I brought my hiking/walking/waterproof shoes, and a pair of dress shoes. Warm, water resistant (Goretex jacket) and jeans, a few sweaters, I think I brought a wool coat too (cant seem to remember) I did not really pack much.
...oh yea, dont forget the swim suit for the blue lagoon!
you will love iceland, it is a magnificant country!