Tempest Strike: Warm Shelter + Blizzard's Wrath (etc) = ...?

Warm Shelter states explicitly that Tempest Strike can no longer proc Frigid Tempest.
Does this effect negate the XX% RNG proc chance granted by Blizzard’s Wrath?

I would assume so. My thought is you can’t proc something you can’t cast. You’d have to test it in game to see though as LE is known for vague tooltips. Some skills explicitly state how they interact and others barely imply it.

Of course it does. You chose a 0 modifier to not cast it. 40*0 is still 0.

You have to be able to cast the ability for the increased % modifier to work on it.