You will need to simply be watchful of the situation and deal with it. Do not place the cage where it will get a draft. In cold climates a draft can be cold and very uncomfortable. Remember, the birds are stuck in that cage. They can not go to a different room to find comfort.
Air conditioning can also create an uncomfortable draft.
Zebras are very hardy birds. Just remember that if you would not like to be where you put their cage, then they probably do not like it either.