Is water icing at the outlet a potential issue? Does this risk decrease if the orientation is upward?

Water icing at the exit of a stack is certainly an issue in cold climates. Significant effort has been put into vent stack outlet design to minimize the probability. Documents such as CGA G5.5 have topworks that are recommended. Stacks that face upward have a higher probability of having water, ice, or snow enter the stack and freeze.