I'm a heavy barrel fan, in any conditions, but alas, it's not for everybody...

That said, I do keep a few options around for hunting short range areas like dense brush or thick woods, in my order of preference:

Number 1 option: Ruger Superblackhawk 44mag with a 4x red dot sight.
#2: Marlin 1985 Guide Gun .45-70 with peep aperture sights and QD 6-24x50mm scope (just in case)
#3: Ruger Mini-30 7.62x39mm with 4-12x40 scope
#4: Marlin 1984 .44mag with peep aperture sights

Handgun hunting is a specific rush, and there aren't many firearms faster handling than a handgun.

The leveraction .45-70 and the .44mag are both GREAT rifles, very light and fast handling, and very deadly. I hand load both .45-70 and .44mag, so I can maximize the power from each cartridge, which are both loaded fairly conservatively in factory ammo.

The autoloader, on the other hand, is a great option too. The 7.62x39mm cartridge is plenty for deer, about equivalent to the .30-30win in power and trajectory, especially in handloads specifically for the Ruger rifle. Coupling the autoloader with such a low recoil cartridge means my cross hairs barely jump off target on the shot, so confirming the hit, or making a quick follow up shot is super easy.

Honestly, I probably prefer the autoloader more than the leverguns as far as LOGICALLY, but usually when I head out to hunt dense brush, I'll take the handgun, then sling the light .45-70 guide gun over my back, just in case I need some extra range.