Shoes - unless you are on a specialized trekking trip it is best to wear sturdy but comfortable and broken-in shoes that are good for walking.
Cold weather - layer your clothing with a lightweight, quick-dry, moisture-wicking bottom layer, a warm mid-layer, an outer layer (jacket or coat) that is wind/rain-proof.
Formal wear - unless you plan to dine at upscale, fine-dining restaurants, dressy attire should not be necessary. You're on vacation so dress casually.
General packing suggestions:
Pack as little as possible and wear layers when travelling.