Yes, Johnkr, some states, typically the more populated states back east have recently passed hunts regs authorizing straight wall case, center fire rifle ammunition. It is a reasonable alternative to using shotgun slugs that are much less accurate. Therefore the .45-70 is a great straight walled hunting cartridge, but it is way more power than is needed for white tail deer in thick brush, and close in woods hunting. Ruger was on top of this situation and came out with the .350 Legend cartridge for lever action rifles. The .350 Legend is a very good cartridge for hunting while tail deer in eastern woodlands.
The question, however, regard the .45 Colt cartridge for hunting deer. In my opinion the .45 Colt is plenty sufficient for white tail deer. In a commercial loading for the .45 Colt the bullet usually is a 265 grain solid lead. A "Cowboy" load normally also uses the 265 grain solid lead bullet but the propellant charge is decreased so that it does not damage older revolvers that may not now hold full pressure. For deer hunting purposes I recommend going with a full up, modern .45 load. A brand new rifle chambered for the .45 Colt has to be able to handle any .45 Colt that is loaded to SAAMI specification by a factory ammo supplier. I have never seen tech specs regarding what a .45 Colt Cowboy is loaded to so I can not even guess if it would be suitable for hunting deer. I encourage a person with a .45 Colt to be used for deer hunting to look around and find a suitable .45 Colt round that is not Cowboy. There must be a number of selections that can be found for such as hollow point, "home defense", and so on.
Regarding the .45-70. I have taken two white tail bucks and two Tennessee wild boars with my Marlin 1895 .45-70. Without question the .45-70 with 305 grain hollow points and with 410 grain lead solids will get the job done. The .45-70 provides an excess of energy on target that really is not necessary. I now live in Arizona, but if I still lived back in Virginia I could be tempted to give the .350 Legend a try on those pesky Virginia white tails. I know what close in hunting is all about, having hunted back there for 20 years. My closest shot was 8 feet and the longest shot was 130 yards.
Good luck with the .45 Colt. Look around for ammo, I am sure you can find it. When you do stock up.