Does FG take into account resistances granted by magic items?

[Vos]

for example a Ring of Warmth grants Cold Resistance. If I am hit with a cone of cold does the AI auto reduce the damage I take?

[TrentLane]

Speaking from a Pathfinder perspective, but it think this is true for most rulesets. The items themselves don't have any effects associated with them, but things like that can be easily coded as an effect; "RESIST: 5 cold" in PF for example.

[LordEntrails]

TrentLane is correct. FG handles these types of things as "effects". Magic Items do not automatically add effects to a character.

What I do is to create an action on the character sheet with the desired effect, put it in a group called "Items" and then have the player add the effect to their character as appropriate. See the wiki and the forums for your ruleset for specific examples.