A 700 Mountain Rifle in most chamberings available,
A 600/660 in most chamberings - I’ll suggest 243, 6mm or 308
A early 700 “carbine” in most chamberings
A 336 Marlin in 30-30, 32 Special, 375, 38-55
A Savage 99 in 250 Savage, 300 Savage, 303
A BLR in most chamberings
A Model 100 or 88 Winchester
A Winchester 94 in 30-30 or more power
Several light 70’s or 77’s.
Then there’s ultra lites and various other rifles from smaller manufacturers

There’s so many good choices!

The best choice is a matter of preference, experience etc.

I have many of these. My 700 7x57 Mountain Rifle is possibly my favorite for conditions you write about. I have a FX-3 6x on top of mine and I’d prefer nothing else.

I prefer classic.
Semper Fi
I used to run with the hare. Now I'm envious of the tortoise and I do my own stunts but rarely intentionally