So for my "nightmare mode" in Minecraft, I want to add a feature where staying in a cold biome for too long will start to slowly kill you, however, this can be decreased by wearing armor, leather being the best at keeping you warm, iron, gold, and diamond keeping you somewhat warm, and chain armor not helping at all. You can also warm yourself up by standing near fire, lava, a fireplace, or a lit furnace for a bit of time. Getting in water or standing on ice will make you freeze faster.
Staying in a desert for too long will also start to overheat you to death, which can be slowed down by wearing less armor, chain armor or no armor at all being the best for staying cool, iron, gold, and diamond being in the middle, and leather armor making you very hot. Standing on ice or in water will keep you cool. Standing near fire, lava, a fireplace, or a lit furnace will make you overheat faster.
So is there any way to make a set of commands to make this happen? Or at least something remotely similar to this?
You can use /testfor or /execute command to do all of those. All though this will take about 50 to 100 command blocks.
*/testfor is for 1.12 and earlier
*/execute is for 1.13 and later
I suggest watching youtube tutorials on how to use the /testfor or /execute command. These commands you are looking for are the basics of the commands.
For example to your cold problem
You can have a repeating command to check if a player is standing on snow/ice blocks. If they are, then have a timer to let's say 30 seconds, after 30 seconds give them a potion effect to reduce their HP.
If a player is standing on snow/ice blocks. But they are wearing armor, increase the timer to let's say 60 seconds, then freeze them after that time.
You can try to display the temperature as a scoreboard score.
Best way for you to learn how to do these commands is to watch youtube tutorials.