Is December a good time to visit Taiwan? Is the weather cold, what is the temperature?

Yes, it is a good time to go there in Dec. You can keep yourself away from the typhoon season perfectly, and there are less rainy day.
Considering temp, the highest in last Dec is 75.2F, the lowest is 48.2F. And the average temp would be around 55F. It may be a little bit cold for you. But it would be ok if you take thick jacket and sweaters to go.