The main reason west coasts of Europe/North America are milder in winters is due to the maritime air mass. The mean flow between 35N and 50N is generally westerly, meaning they are largely influenced by the water to the west. Conversely, central/east coasts of continents (Asia/North America) are influenced by continental air masses, so it is colder in the winter, and hotter in the summer (land gains/loses heat faster than water).
As far as the Mediterranean is concerned, the main reason is due to the Alps, which prevent cold air masses from penetrating so far south. This, combined with the fact that there is no true arctic/polar cold air source region over northern Europe (due to the Gulf Stream waters west/north of Scandinavia), means cold air outbreaks are rarer than in North America/eastern Asia. The cold air would have to originate over Russia and move west/southwestward. Since again, the mean flow is from the west, this doesn’t happen very often. So, cold snaps are occasionally experienced over northern/northwestern Europe, but very rare (I’m not sure how rare) south of the Alps. So, this explains the warmer air generally in the winter. In the summer, the area is fairly similar to other similar latitudes, which also heat up pretty rapidly.