Do variable venturi carburetors ice-up?

I understand that carburetors would tend to ice up under cooler ambient conditions without preheated air, but it seems to only affect the fixed choke type. How about the variable venturi (also known as variable choke or constant vacuum/depression) carburetor?

Any carb without sufficient heat will ice up, in low temperatures and high humidity. A VV carb may be more susceptable, given the extra moving parts, but icing can quickly ruin the performance of any carburetor.