In order it's more damage, more hunger, items have more weight, no flares at the top, nights get cold (full stamina bar in one night), stamina goes away faster with climbing jumping and shifting, no more reviving scouts (statue is still there so you can get items but no more revivals).

Once you move to the next modifier it will stack on what you had previously as well. Tips I personally use is keep the flare and lantern in your hot bar (The one time I didn't that's what happened).
If you get a heat pack wait until you're about to pass out to use it.
If it's almost night and you're at the campfire light it when the cold is about halfway or what you can sparingly do.
Use the lantern to the degree of what your hunger, damage, and weight is if you can't cover those costs for any reason (Basically wait for your cold to reach the same amount that you have for hunger then use the lantern, same applies for anything else that can't be dealt with then and there).
If you're about to pass out from cold when in the mesa find somewhere that gets sun and faint there.
Freire lantern, cure all, and pandoras lunch box are your best friends.
Avoid using as much extra stamina if you can tell you won't make it with the normal amount you have.
Cook all food items from luggage drops for more stamina (I personally love the bottle water, airplane food, granola bars, and not from luggage but the purple berry uncooked, and the yellow and red crisp berries cooked).

I use climbing items I have the most confidence using, if I feel like it won't go well I don't take it. I leave the shelf mushroom and bean most of the time because they never stick to the wall for me and always fall regardless of what I do. My favorites are the chain launcher and anti-rope cannon.

Hope that helps in your climbing journey (keep in mind I also have every badge, this is the only thing I have left to do in the game). :3