Don Durito
Hero
The default rules do tie ability rolls to skills, but then they also don't include Endurance, so if we're changing things...It's passive to the action but you are Actively invoking your Endurance.
Athletics (Con) is the better way to do it but the default rules ties skills and abilities.
Actually that's an issue I have with 5e.
You are talking about Medieval to Rennaissance level tech. Travelling the world to adventure would involve a TON of Endurance checks due to weather, climate, resting spots. long marchs, and poor sleep.
To me the test of whether something should be a skill is "is there anyway to directly leverage this to accomplish your goals" as I suggested above in the city example. I played through enough 4e skill challenges where Endurance was my best skill to know how difficult it is.
Ideally you would divorce the ability scores from skills formally (the 5e system is designed to make this easy it's just that playtesters balked at removing formal skills).
Make endurance part of Mountaineering and include climbing things, and skiing and navigating, or merge it with survival or something. (Who has Survival? The Ranger and Barbarian, who should be good at enduring outdoor conditions? The Ranger and Barbarian).