Hi! I am currently studying in Dublin and there are many things to do in the winter there! However, your main issue will be the lack of daylight. In the dead of winter, it can be almost pitch black by 6pm and doesn't get light until 9/10am. This means you will want to do all your siteseeing in the middle of the day and save any pubs/restaurants/inside things for the evening. Also, most shops and museums will close by 5/6pm. Dublin does not get extremely cold, maybe down to 0C if they are lucky, but it doesn't normally snow, so if you are looking to hike or drive around the countryside, you will only have to deal with rain (most likely).
In the winter, there are usually Christmas markets running in the city center and there are lights all over the city and covering Trinity College which can be lovely to walk around and view. I recommend grabbing a hot whiskey at a pub and listening to some traditional music!