There is another elephant in the room that you shall consider, concerning not how the checks are determined, but their frequency. In situations of extreme cold or extreme heat, for example, you have players making checks every hour. Were they to travel half a day (a typical "montage" for traveling purposes, you would be asking them to literally 4 or 5 dice (potentially more if it is an entire day of traveling) that are the same exact check with maybe a slight increase in DC as the hours linger on. In an hour by hour approach this type of check is fine, but in longer situations this WILL slow down the game substantially.
For example, when I ran a Reign of Winter game awhile back for the pathfinder system, this was a large source of annoyance for both my part and the players, and failed horrendously at capturing the feel of "hardcore wilderness" feel we were going for in the first place. All it really accomplished was bogging down the game and making "unfun" for all of us. Now, obviously, this was all different system (one in which fiddly bits are more welcome, and which I did have), but the principles of much of it still applies.
One thing I would consider doing for the sake of game flow (all what I indeed did for the above campaign) is to have the players make one check and base the hours traveled on the lowest die roll (i.e. the "weak link" in each case). I would then tell them how many hours had passed and that that player had then gained a rank of exhaustion, giving them the option to then rest or use magic to reduce it, or press on, reroll, and likely have that exhausted player slow them down. Once they travel 8 hours, they typically will rest anyway, unless they are in a hurry, in which marching rules come into effect. For the other system game, this caused them to still feel the effects of the cold/heat, as it caused them to go less distance each day (or risk a player being seriously crippled), but kept the game moving without rolling a bunch of unneeded dice.