The weather over the past couple days has reminded me that you can freeze your ass off, even in Taiwan. No matter how often I get to rub in our great biking weather to my friends in North America, or Taipei for that matter, I still have to face the fact that we do get some cold spells from time to time. Fortunately, it doesn't stop me from riding.
When I ride in the mountains or on colder days in Taiwan, I found the best strategy is to use layers. Sometimes the temps fluctuate enough on a ride to strip down to short sleeves, or wrap up for warmth. Packability is key to choosing the right gear. You should be able to stuff everything in a jersey pocket.
The single most important factor for Taiwan's cold temperatures is wind. The winter wind really makes all the difference. Therefore, I use a really great Castelli windbreaker. It is amazing what a thin layer of windproofing can do to keep you warm. Often, that is all I need over a jersey. My wife likes her Pearl Izumi windbreaker as well. Hers is florescent yellow for visibility.
Both jackets keep a low profile to prevent unnecessarily creating drag. The last thing anyone needs when cycling head into the wind is any more resistance.
For really cold days I use a Craft base layer that is amazing. It is thin enough to see skin through the fabric, but it traps warmth. Totally recommended. It hugs the body, so it will not bunch up or rub. I just wear it right under my jersey.
Some other weapons against cold are my arm and leg warmers.
The Adidas arm warmers are cheap and work well. The Assos leg warmers stay in lace and really haven't warped since I bought them a couple years ago. For the coldest days I just slip the arm warmers over the sleeves of the base layer.
The rule for helmets is you always pay more for less helmet. I guess I paid a lot because I have quite a breeze that blows over my head when I ride. Therefore, I picked up a couple hats of different thickness. The thickest hat is my Nike thermal skull cap, but I have another one I got at an outdoor store that is really nice too. The important thing is to make sure they'll fit inside a helmet. Your helmet may fit fine as-is, but put too much hat in there and it can be uncomfortable.
The last adjustment I make for the cold is a pair of long-finger gloves. I got these Assos gloves that are actually summer gloves, but they work fine on Taiwan's coldest days. They are great for those in between days where it is freezing in the morning and then warm in the afternoon.
That's about it. You don't need much, but just enough.