That boy just ain't right. Hunting deer with a shotgun would land his butt in jail in Texas. Okay, being a flaming lib from Mass. is enough to land his butt in jail.
And using a rifle in many states and areas within states would land your butt in jail. I have 75 acres in Coventry NY (a little outside of Binghamton) and we must use shotguns. But, travel a little further north and you enter "rifle country" where you can use either a shotgun or a rifle.
And for fun, my uncle will hunt deer with a handgun sometimes!
Actually, I don't think it would. From the Texas Parks and Wildlife hunting regulations:
Means and Methods
Firearms
Game animals and game birds may be hunted with any legal firearm, EXCEPT: • white-tailed deer, mule deer, desert bighorn sheep, and pronghorn antelope may NOT be hunted with rimfire ammunition of any caliber.
So It would appear you can take your 12 gauge and shoot a deer or sheep legally in Texas. I'd recommend rifled slugs or better yet sabot type slugs and a rifled barrel. You can also take your Desert Eagle and shoot 'em with that. It's certainly plenty of gun for the whitetails.