Tales and Chronicles
Jewel of the North, formerly know as vincegetorix
I think the Exploration Pillar covers a lot more than is usually granted.
For example: navigating a dungeon, searching for treasure, and managing traps are all navigation. They also offer opportunities for characters to be good at their skills and tools, like Perception and Thieve's Tools.
For the overland travel side of Exploration, I long ago gave up on trying to implement a cost. The truth is, between Utility Magic, Goodberry, and outdoor backgrounds, the characters are usually going to find ways to be rested and fed.
Instead, I try to add opportunities in overland travel to gain rewards: treasure, knowledge, allies, etc.
If a DM switches Random Encounters from "a chance to lose HP" to "a chance to get more treasure," I think players will enjoy them a lot more!
This is a great idea.
Searching for a hidden cache in an abandoned roadhouse during a terrible storm is way more than yet another encounter against gnoll brigands.
Or DM should try to target different resources than HP.
Let HP be the resource you track for battle. Make them lose HDs due to the strain caused by a blizzard, gaining more than 1 exhaustion level, give them diseases or poison that only allow a save after X days, reduce their max hp until X, reduce their speed until X, steal their equipment while they sleep etc
Given, some classes can circumvent those things at mid-high level, but that's the prerogative of higher level PCs.