This is not really so much a hack as it is probably errata material. A ring of warmth (DMG 193) is an uncommon magical item. A ring of cold resistance (DMG 192) is a rare item. However, a ring of warmth does the same thing as a ring of cold resistance and also protects the wearer in low temperatures.
Easy fix: A ring of warmth is a rare magic item. This probably will not come up often–if at all–in your game. But if you allow your players to purchase magic items (DMG 135), this might be something to consider.
But… what do I know…?