The .38-55 Winchester factory load (do they still make this?) is/was very mild. Something along the order of a ±250 gr. bullet @ ±1350 fps. In the Marlin "Cowboy" rifle, it ought to be very pleasant. Buffalo Bore makes a .38-55 that puts it in the same general class as .35 Remington or .375 Winchester. Not exactly a bone crusher (for the shooter) but a very potent woods cartridge.
Winchester still makes factory loaded ammunition for the 38-55. In a 26 inch barelled model 1894 rifle with a full lenght magazine tube the recoil would be considered moderatly light. In a model 1894 (94) carbine however, the recoil of a 255 grain factory load "will get your attention". The old 38-55 was first developed as a black powder single shot rifle target round, and along with the 32-40 was one of the best and most popular cartridges ever developed for that purpose. A very accurate cartridge in a model 1894 rifle and more than adequate for deer and black bear in the woods.