I agree that the weather will be better in the May - September months, but I went to Ireland the first week of December a few years ago and very much enjoyed my trip.
Airfare, rental car (upgraded to an automatic), 1 night in a hotel, 5 nights in private bath B&Bs, and the last night at the Dromoland Castle, plus the taxes came to just under $750 per person. It was a fantastic deal!
The only thing to note about the winter months is that days are shorter, and, the closer you get to Christmas, the fewer places are open. However, we spent zero days bored or disappointed. The weather was quite similar to the temps. we'd left behind in Texas (low to mid-50s), and it only rained on us one day. (Since we'd purchased London Fog Overcoat Raincoats and knit caps, we were fine to sight-see in the rain.)
My point - if you are on a tight budget, visiting in winter certainly won't be a letdown...but, if you have the money, you would probably do better by going a little earlier in year.
Gorgeous country - and a highly recommended vacation to anyone.