From MCW (Powder Snow):

Wearing any piece of leather armor stops the freezing effect and reverses the damage. This applies to entities that can wear armor, such as players, zombies and horses wearing leather horse armor. If the leather armor is put on while the entity already has the freezing effect, the effect fades away the same as if the entity exited the powder snow.

Seems to be handled by an item tag, freeze_immune_wearables. On a related note, trimmable_armor may need to be added as well to allow burlap armor to have trim added to it.