The best way to keep warm is to have a few layers of clothes, not just (not even) a big thick coat. If you have a cotton TShirt, a normal shirt or blouse and a light jumper or sweatshirt underneath a normal coat you will be warm enough. Basically what you wear at low altitude is fine, just extra layers of it, so take loose fitting stuff so you can add it on top of each other.

Large branches of Migros will sell all this stuff and Manor is also a reasonably priced department store. As it is just becoming Spring most shops will be switched over to sell summer clothing. This means limited choice, but you could find some old season stuff discounted. You won't find much at the station, it's better to go to the main shopping streets.