October in Taiwan is usually one of the most pleasant months to visit as conditions tend to be warm and dry, yet cool in the evening. Fall is from mid-September to October, winter generally runs from November to February. Typhoon season is behind us and the humidity has dropped to a pleasant range. Average temperature is about 25C in Taipei, but gets down to about 12C if you go to the mountains. Those of you from cooler climates, may feel warmer than those from the hot tropical places, so bring comfortable, informal clothes you can add layers to if needed. A light jacket, sweater or sweat shirt is a must.

Information from weather.com

http://www.weather.com/?from=globalnav