I've cycled mostly within ASEAN, went cycling in Taiwan recently. It's really cycling friendly in terms of infrastructure and cultureIt's got mountains (cycled up 2,600m), plains, road and offroad. Story here: http://lifecyclesg.blogspot.com/2012/01/taiwan.html
I just finished reading your report and shared the days and photos of your trip in Taiwan. I am very happy for you that you have been there and got to know how incredilbly friendly the Taiwanese were. The taxi drivers probably not Taiwanese.
I think I wrote somewhere here that no one cycle in Taiwan during the winter. I would not. I guess since you from Singapore, you would not have known how cold Taiwan can be in winter. Your cycling there in winter not counted.
Taiwan winter is miserable because cold together with humidity can really hit hard. And to read you cycled up Alishan in winter! I can only smile when I was reading your report. The good thing about Taiwan in winter is that there are hundreds of good hot springs, where I spend much of the winter in.
I found staying in other countries with -10 to -20 was less cold than Taiwan. Largely because when the temperature drop below 0, moisture came out of the air and dry cold air is ok.