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:
When renting a car, inspect the vehicle with the sales rep and document with photos any dents, dings, or damages prior to leaving the rental company to avoid any back and forth on its return.