@jaybray , when I start a hunting bbl up and I don't know the answer to your question, I start by making a test out of the real world. Once the load development is run, I will intentionally stop cleaning at some point and just use the gun. Every so often, I will throw it on the bench and test a group and keep good records. I will take a good long look with a borescope and then decide if I will clean to avoid carbon build-up, or when I see a group change or POI shift that ammo doesn't explain.
When I get to an elk hunt, we usually start with a clean bbl and it gets fowled checking boresight before we set out. I use a piece of electrical tape over the muzzle when I walk around, and replace it soon after a shot if I can. That keeps dust, twigs, seeds, mud, snow, bugs, etc, from getting involved. Too many folks get junk and mother nature in the muzzle while hunting and don't even realize it.
Prairie dog trips taught me a lot. You get an opportunity to shoot a bunch of rounds, and then test in a low key setting to see how far you can push it before you have to stop and clean. The main difference with PD trips is the round count goes up all at once while the bbl might be warm, as compared to a predator rig where the bbl cools down between short sessions. Then there is elk hunting where things can go from below zero or dripping wet, to warm trucks or hotel rooms, then back out again for a week or more.
I used to shoot silhouette when I was younger, and that also gave me a testing ground where I learned that stock REM bbls could be night and day, with some going over 100 rounds with no issue, and others that could hardly make 40. I know I can run 250 rounds or more through a White Oak AR upper with no issues, and then I give it a light cleaning and keep going. Elk sporter bbls I clean after the season or sooner if they get really wet.
I tend to run a dry patch if I have a hunch that the humidity or dust has become an issue. If that dry patch comes out very dirty, then I punt and clean the rig as long as I know I can fowl it before taking a critical shot. Because I run with tape over the muzzle, that doesn't happen much unless it gets dirty through the breach while loading and unloading. Any rain or snow on the ammo is minimized if I can, but if that is how the day runs I will dry patch the chamber at the end of the day.
Hope that has given you a few things to ponder. Good Luck and Good Hunting.