We are planning to hike and visit Taiwan by second week of March 2018.

TW is a big province, so I can only you the weather in Taipei as an example.
According to former data, the temperature may range from 10C to 25 C, and there may be some rainy days, it hardly snows at that time, so you are suggested to take your shirts, light coats, and jeans. Thermal clothing is not needed.