On the whole paphos is far more of an all year round place for jobs than many of the areas on the Eastern side of Cyprus.
Hotels do not close down but some of the bars in the tourist areas close for January re-opening again mid February.
As for weather Februay and March are wet but temperature wise like a warm spring in the UK. When we go down to the tourist areas at that t ime of year although we might be dressed in jeans and sweaters the tourists are in skimpy summer clothing.
Veronica