Thanks, TallIan, I'll give some thoughts to your suggestion. I've made some changes to my original proposal. This is what I have now:
Extreme Cold: Surviving in extremely cold or hot places, like arctic or desert climates, can be a challenge. If you are in an arctic climate and have no cold-weather gear on, you are going to slowly freeze to death. You must succeed on a DC 10 Con saving throw each hour or suffer a level of exhaustion. At nighttime it becomes a DC 15 Con saving throw every hour. If you have cold weather gear on (thick coat, gloves, boots, head covering), then you automatically succeed on the saving throw while traveling (the physical exercise from moving also keeps you warm).
But at nighttime when you are camping, you will have to succeed on a Con saving throw to survive the cold weather. In cold weather, the DC is 10. In very cold weather, the DC is 15. And in extremely cold weather, the DC is 20. Having a tent or some other form of shelter gives you a +5. Having cold-weather gear gives you a + 3. And having a bedroll (which in our game is a thick, wool blanket) gives you a +2.
Extreme Heat: If you are in an extremely hot place, like a desert, you will need to consume twice the amount of water that you normally require. If you don’t have access to drinkable water, you must make a DC 5 Con saving throw for the first hour, or suffer a level of exhaustion. The DC increases by 1 every additional hour. Characters who are wearing medium or heavy armor have disadvantage on the roll. Character who have drinkable water but are wearing medium or heavy armor must still make a DC 5 Con saving throw, increasing by 1 every hour, but they don’t have to make it with disadvantage if they are drinking water.