Rama, some places in Italy, and most Aegean Sea islands of Greece do not have cold air in January and February. But there could be rain at any place in Europe in January and February. Being at an island of Greece is not enjoyable when there is rain.
Cities that I think could be enjoyable to visit in January and February are Salzburg and Vienna in Austria. The museums there, and the palaces in Vienna,are open in January and February. I saw a video travelogue of Salzburg in February. Big fluffy snow flakes were falling from the sky on old town Salzburg. It looked pleasant. The air is usually not very cold when there is snow at Salzburg. The hotels probably cost less in January and February, compared to most other months. In Italy at the Cinque Terre (Mediteranean Sea coast) the air can be warm in February, very pleasant. Read the books "Rick Steves' Italy", and "Rick Steves' Germany and Austria", and "Rick Steves' Spain".