Visiting Taipei in the period of Dec 20 to Jan 9. What should I be prepared for?

We are coming in from a tropical country and we are just worried of what type of winter apparel should we get. What exactly is the weather like there during our visit? Do we need really thick clothing or just mildly thick? Is it insane to test out the weather only when we land wearing sweaters and long pants with shoes first? We plan to buy any winter apparel only when we reach Taiwan as it is more cheaper there compared to tropical countries. What's the best way to prepare here, guys?