When is the best period to go Taiwan in 2016?

The best time is between Nov. to next Mar. Avoid the typhoon season from June to September. Have a great time!

I see, however it's the winter season during that period of time right?

Yes, that is right. Although it is during winter, the temperature won't be very low. On the contrary, you will generally feel comfortable to travel both for outdoor and indoor activities.

Alright, I am just worry about the clothing that they are selling during winter, it might not be suitable for me because Singapore is always summer season. Actually, I am thinking if going during October will it be suitable?

Actually, there will have many heavy rainy days in October. It will more or less influence the sightseeing a lot. So it's still suggested to go there between November and March. The climate may still warm at that time. Just prepare light jackets, long sleeves and jeans. If you don't have these clothes, you can buy some when you arriving. Many stores sell seasonal clothes. Don't worry.