You won't freeze at all if you bring/purchase the following (for general urban hanging around): wool socks, long johns, proper boots. However, if you wish to go to a bar/pub, those long johns can get hot. It also helps to dress in layers, let's say you bring your favourite hoodie, definitely have a t-shirt under that and the jacket, but if it's cold and you're going to be outside, a thin shirt between the tee and the hoodie will help immensely. Also, a scarf is highly recommended, also a hat.
Alcohol restrictions: Got to be over 18 to buy alcohol and tobacco, and over 20 if the alcohol you wish to buy has over 22% alcohol content. Except the last bit doesn't apply to a bar, I suppose.
Grocery stores can only carry beer, cider etc up to 4,7%, everything else you have to get from the state monopoly Alko. And only drinks that have been made through fermentation can be sold in grocery stores, so if you wish to try the lovely Finnish lonkero, the one in the grocery stores is not the proper one.
Bars and stores start serving alcohol at the same time, 9 in the morning, and stores stop selling after 9 in the evening, Alko however closes at 8, and 6 on Saturday. It's not open on Sunday.
Also, some of feel that the price of alcohol is a bit of a restriction...