How I do Cold Exposure damage in D&D 5E

I modified the exposure rules in Pathfinder on page 442 of the core rulebook and added it to a 5e spin.
My players are 8th level.

Party members are climbing hook mountain to get to a tribe of ogres. Climbing the mountain is simple enough but a few survival checks will get the party on a path that the ogres use very frequently. They could also try and avoid patrols by climbing.

Exposure to the elements is unused in D&D 5e, at least in my games, but I will change that and make the group fear mother nature. In this three hour journey along the trail they may have a random encounter but the way will be swift up the mountain, but if they decided to climb it will take 6 hours and they will get up without encounters but exposure and falling down the mountain may happen.

Rules, Failure does not mean instant death, but slow or very little progress up the mountain.

Climbing,
DC 14 Athletics check every hour for six hours to climb the mountain (advantage with climbers kit or creative methods (spells,equipment,player wording,etc..))

Search for Trail,
DC 15 Survival check, a success means they find the trail to walk up the mountain in three hours but they have a 30% chance of a random encounter every hour. Reduce percentage chance by 15% for creative RPGing (using stealth, slowing the pace down, using spells,etc,etc...)
Players will use HELP, in my games I allow the HELP action which gives advantage to skill check rolls.

Player's Handbook page 291 has the exhaustion chart, the group will make Constitution Saving throw DC 13, for cold weather under 40 degrees F (4 degrees C).
Partial Winter clothes gives advantage, fully clothed winter clothes (gloves,hats,boots,etc) as do spells that protect against the cold that last one hour requires no roll at all, you succeed.
Each hour of exposure adds +1 to the DC.
Hour one DC 13 Con save
Hour two DC 14
Hour three DC 15, etc...

Each failure does 1d8 Exposure damage, not actual Hit Points but exposure damage.
How many Exposure points do I have? your current H.P's divided by six, why six? Players Handbook page 291 has six levels of Exhaustion.

A 8th level Cleric should have, with a Con stat bonus of +2, 59 HP's at level 8.
59 divided by 6=9.83 round down, 9

First hour of exposure if failed results in 1D8 Exposure damage, lets say a six is rolled.
Second hour of exposure is failed as well, resulting in a further roll for exposure damage, resulting in another six of exposure damage, total 12.
That is below the 9 for level one, which results in level one Exhaustion, disadvantage on ability checks. Level three pretty much would kill the character unless they get out of the cold weather.


Quick google search and now I re-skin each level by using these words to describe the effects,

What are examples of 'nonfreezing' cold injuries?

Chilblains are a mild cold injury caused by prolonged and repeated exposure for several hours to air temperatures from above freezing (0°C or 32°F) to as high as 16°C (or about 60°F). In the affected skin area there will be redness, swelling, tingling, and pain.
Immersion foot occurs in individuals whose feet have been wet, but not freezing cold, for days or weeks. It can occur at temperatures up to 10°C (50°F). The primary injury is to nerve and muscle tissue. Symptoms include tingling and numbness; itching, pain, swelling of the legs, feet, or hands; or blisters may develop. The skin may be red initially and turn to blue or purple as the injury progresses. In severe cases, gangrene may develop.
Trenchfoot is "wet cold disease" resulting from prolonged exposure in a damp or wet environment from above the freezing point to about 10°C (50°F). Depending on the temperature, an onset of symptoms may range from several hours to many days but the average is three days. Trenchfoot is more likely to occur at lower temperatures whereas an immersion foot is more likely to occur at higher temperatures and longer exposure times. A similar condition of the hands can occur if a person wears wet gloves for a prolonged period under cold conditions described above. Symptoms are similar to an immersion foot.