I think cold dmg is checked against resistance every time you land a hit. If the resist fails, the dmg is added like a DMG Bonus is added: on top of your normal damage for that hit.
For instance, let's take a character wielding this with a dmg bonus of 6. On a succesfull hit of say 20 dmg, the 6 dmg bonus is added, a Cold resistance chack is made, if it fails the cold dmg is added.
so: 20+6+3=29 dmg
Hope this helps
Yrion Shadowhand
killer of stuff