Pacha is the only club that's open all year and even that's only for weekends through the winter. Amnesia is generallly open new year's eve along with Underground. Space used to be open but hasn't been for the last couple of years.
It is all very different. Amnesia, for instance, is full of locals who can't afford to go during the season. What makes it particularly strange is that traditionally everybody dresses up and sees the new year in with their families. Then they go out. So Amnesia's full of all these guys in their teens and twenties dressed in dark suits and ties.
Most hotels are shut for the winter because they don't have heating. Most of the bars and restaurants which cater for tourists are also shut. You'll just find the odd bar open in the West End or Ibiza Town Marina. If you are staying I'd suggest you try for somewhere in Ibiza Town.
That said I really enjoy new year, three kings, carnival, semana santa and all the other excuses for parties that people find through the winter.