You can't post that picture and not tell the story, BrentDMy hunting Sharps, a .45-100 (2.6") has a 32" Standard weight barrel which is 1/2 octagon. It carries just fine and it slings just fine as well. I haven't tried it on a horse. Personally, I would not go shorter than 30". For a lot of reasons, I like 36" sight radii, but it has nothing to do with longer being better. Just simpler math.
How it balances depends just as much on barrel weight and profile as it does on length. You didn't say what weight or profile (or I missed it).
the "handiness" of short barrels in the woods is much overrated in my opinion, as is the overwhelming advantage of longer sight radii. However, shorter barrels do have less fouling issues, and that is NOT overrated entirely. The 34" barrels are well known to foul out of matches where the shooting is fast and hot. This is not, however, a big issue for a hunting rifle.
Buy what pleases you. Any length barrel will kill the same number of animals with the same number of bullets, so barrel length won't mean squat with regards to what ends up in your freezer.