Winter Time - Travel Experience

a) Not that likely. At least it won't stay in most cases as the temperatures won't stay below 0 °C long enough. Esp. at the sea ports rather unlikely (as the sea will still have around 10°C this will also warm up the environment a bit.).
Good chances however in the Harz mountains (between Berlin and Hannover).

Average temperatures are such a thing. 0 °C could be the mean from -5 °C and 5 °C. Or from -15 °C and +15 °C. Latter would be already unusual but not impossible. And than there are the +felt temperatures. Dry and sunny -15 °C are more comfortable than wet and windy -5 °C.

b) Dress in layers. As a tourist you will rather frequently switch between heated places and the outside. Important are good shoes. I.e. that you don't get cold and wet feet on the first encounter with snow. And you need a wind and water proof jacket.

c) Holiday season: yes. But no business season (conferences, trade fairs etc.). Thus no peak season for accommodation - apart from around New Year (big party) in Berlin. However a peak season if it comes to transport (full trains, traffic jams etc.).

b) if you have "normal clothes" just buy a pullover and a waterproof jacket. But even some Germans don't always go with wind and waterproof jackets and 10 layers (though they normally don't walk for 5 h outside then. ;)

Can't speak for the cities at the coast but Berlin can be mean in winter, temperatures can easily drop down below zero often there's wind and if you plan on seeing the city, dress up appropriately. Warm shoes are the most important thing, dress in layers, scarf, mittens, wooly cap (keep your ears warm), in short bundle up. December ist the time for christmas markets in Berlin so there will be tourists but not too many, visit the one at Gendarmenmarkt, they charge for entrance but it's only about 3 Euros and it's the most christmasy and seasonal market.