armor +10 vs cold attacks

i found a shield with +10ar vs cold attacks . does this reduce damage from ice spells as well or from weapons with ice mod only ( e.g. icy dragon sword ) ?

It's all cold damage so I'd say it would reduce for spells and weapons

16 armour vs physical and 10 vs ice/water damage is my guess

Any cold damage. This includes spells that do cold damage, and wepons that deal cold damage, because cold damage = cold damage.

Well, conditional armor always makes a reference to attacks when in reality they affect all damage. It's the only time "attacks" doesn't just refer to weapon attacks and attack skills.

Sorry, wrong guess. The 16 armor of the shield is not limited to physical and the 10 vs. cold dmg is in addition to the armor of the shield. So:

26AL vs. cold damage
16AL vs. all other damage affected by armor