I have changed some things in my conditioning routine this year.
I am taking walks 5 days a week before work in the morning with a heavy pack. I have worked up to 4 miles with a 70+ LBS pack. I can feel that workout in my legs, hamstrings mostly. I think this will make carrying heavy packs of elk meat easier.
My wife got us a family membership to a local gym. She doesn't use this but I do. I try to go 4 nights a week after work. I do deadlifts and barbell squats one of those nights. I can really feel the barbell squats in my thighs: I'm hoping that will make climbing easier. The deadlifts are probably making my back stronger, but that has not been a problem in the past. Monday, Wednesday, and Friday evening I spend 30 minutes on a recumbent bicycle. The last 15 minutes I am breathing hard and am dripping with sweat (level 16, but I don't know if that level is consistent across diffeent machines). I follow the bike with various other exercises with weight machines and climbing stairs with a 30 LBS dumbbell in each hand.
I'm hoping to add some other exercises into the mix. For example, I'm looking to start doing a "farmer's carry" soon.
I'm working on strengthening my grip. I find my hand gets tired sometimes when skinning an elk. I grab the skin in a wad and put tension on it with my left arm while slicing the skin free with my right hand. It is kind of a thick wad, and I grip it fairly tight so I can skin faster. I'm doing wrist curls with 45 LBS dumbbells, some wire cutting with wire cutters, and pinch grip work with landscaping blocks.
I always get out of breath climbing the hills. I accept that. I train so I can keep going day after day: endurance. I train so I can climb the hills without giving up, though I stop to catch my breath. Also, I'm hoping the heavy pack walking exercise is going to allow me to carry a heavier load of elk meat this year. I carried an elk ham last year -- probably about 55 LBS -- back from my kill site. I found that manageable. My goal is to be able to carry even more elk meat than that at one time this year. I've got an improved pack that should distribute the load well, and I've been training my legs to the packing work.