The 1858 Remington black powder loads are anemic by today's standards. If you were wanting to try hunting with it, I'd deligate it to small game only.
For deer, the Ruger Old Army with max loads and a bullet or the Walker Colt Repro with a round ball holding around 60 grs. of black powder would be a better choice and might work.
Even then, only close shots, 30 yards or less, should be taken. Practice alot too. Just my opinion based on my shooting experience with black powder revolvers(35+ years). Never have hunted with one though.