What do I bring to Taiwan?: Cool weather wardrobe check

We often get asked by people moving to Taiwan what they should bring.  It's a hard question to answer.  But, as we go through this second year I'm able to get some perspective on the things that we found important.  I'm hoping the "What do I bring to Taiwan" posts can help give some ideas to those moving here about what to pack.

Last year at about this time I started wishing that I hadn't filled my bag with only shorts and tank tops, because it started getting chilly outside.  And worse than that, I quickly found out it was often cooler inside than out (I guess when you have tile floors and concrete walls you should expect the cold to stay).  We're more prepared this year - each with a few long-sleeve overshirts and sweater/sweatshirts.

The last few days it has cooled down a lot in Taichung (currently 67 wunderground says); people are bringing out their pants and sweaters.  Not this cold yet though:

Cool rainy day in February