If you are talking a dedicated hunting revolver as a primary weapon and not a "backup in case they are close", I'd stick with a 6'' tube or greater. Could be a a tad biased, but I'd also consider something like a S&W P.C. version made just for hunting. I have a S&W P.C. 629 Lew Horton .44 Magnum Hunter that is a favorite of mine, but I have taken deer also with a 6'' 686 in .357 along with the P.C. X-Frame in .460.
Do you reload? If not then I wouldn't consider the .41. While a .357 is sufficient, the .44 is hard to beat. Unless you are familiar and proficient with handguns and do reload, I don't suggest anything bigger. .45 Colt may or may not be in that category. While it is a good deer cartridge, factory ammo is generally directed at C.A. usage and not really good for deer. That little bit factory hunting ammo out there for it is hard to find and expensive. Factory .44 Mag ammo is plentiful and hunting rounds much more reasonable. If you reload, or have deep pockets starting out with a .45 Colt is not any different than starting with a .357 or .44 for deer. But handgun hunting is not like rifle hunting. You must practice a lot, and often, in order to keep the proficiency needed to hunt deer. Unlike a rifle, you can not put it down at the end of the season and then pick it up the week before the next season and put 3 or 4 rounds downrange to make sure the scope is still on. That is the main reason I always tell folks to consider the price of ammo when considering what caliber of hunting handgun to get. If the cost of ammo is prohibitive, odds are, you won't practice enough to ever see your or the gun's potential.