The North, sure, is cold at that time of the year and at some altitude, but it is worth it.
Sapa in January can be very cold, especially at night, but remember that it will be the dry season then, and you will ride most likely with the sun warming you up enough. In the winter time, there can be some really nice shiny days.
Do not forget to bring with you warm cloths though.
If one must choose for a 3 week trip, then the North is much more interesting : scenic mountain roads and landscapes, more lively people.
And absolutely not to be missed is the North of Hagiang loop