If there is freezer burn on the skin should the skin be exposed?

Not possible: Freezer burn is the drying of food in a food freezer (by sublimation) by a type of evaporation which dries out the food. You would have to put some part of your body in a freezer for months for this to occur - and other things are much more likely such as frostbite.

Unclear but: I suspect that your question was related to skin damage from ice or dry ice. If the lesion is not open, just let it be exposed. If it has breached the skin surface, you may cover it but be sure to keep the area clean.