This ring protects you from the ill effects of travel in cold climates. You will feel the cold to a more limited degree but not suffer from exhaustion or frostbite. You will not shiver and all reactions and other abilities will be as if you were in a cool but comfortable climate. Since the ring only brings your body to a stable state in wintry conditions, you still take cold damage as you would without the ring: it grants no damage immunity or resistance. 

The ring does not 'add' heat so wearing a winter coat or sitting by the fire will still feel better to you (see above about still feeling the cold) but you won't over heat due to the coat or the fire. As such, wearing the ring in warmer weather does not create any negative effect. The ring simply is a ring in those climes. The ring will not reverse damage or effects should you suffer from them prior to wearing the ring i.e. if you have exhaustion or frostbite from traveling in extreme cold and then put on the ring, it will simply prevent the progression of those effects. You will still need healing for the frostbite and rest to overcome the exhaustion. 

Notes: Immunity: Cold, Utility, Jewelry