It depends heavily on the ground.

Walking through knee-deep mud or nearly-molten snow costs a lot of energy just to lift your feet.

Another aspect is water. In a hot, dry climate you have to carry water to prevent dehydration.

I don't know about realy cold, dry climates, but I guess there is the same effect from the other side: you would lose moisture by some kind of freeze drying, giving off warm, moist breath but breathing in cold, very dry air.