Preacher Curt,
I have no experiance with a 44-40 Henry, but in 2004 I harvested a Doe in the Wisconsin early antlerless season using my 58 Rem with .45 Colt Conversion Cylinder. She was at 25 paces and broad side. She went about 15 yards and dropped. The 250 gr Winchester factory bullet went clean thru. When I dressed her out and recovered the the heart and liver the heart had a perfect hole thru it. I was lucky she was at my practice range of 25 yards. The huntin regs for deer in WI state that the caliber be center fire , .25 or larger with at least a 5" barrell. I was the talk of the early season deer camp that year.
As for the 44-40 Henry, Just practice,practice, practice. She should be a fine Deerslaying rifle
Regards
LoneGrouse