Which bow upgrade is best for..

..the ring of fire? Right now mine does shocking damage, would it be cold?

It's cold damage, but you could always bring Winter and all elemental damage would become cold damage. It's got a global effect so those fire nukers in your party would deal more damage too.

i have heard of winter, but i don't know where to get it, do i have to cap it?

It's a normal skill so buy it from the skill trader in Ember light Camp.

IIRC, you get Winter from a skill quest in the Northern Shiverpeaks. Why waste all that precious gold on a skill that you could be donating to the 'Make Stormlord a rich bugger' charity drive?