I do not know anyone who hunts deer using a pistol. But perhaps in Texas things are done differently.
I can tell you that cartridges I reload for 7.62x25mm Tokarev pistols use only around 5 grains of Titegroup powder and send a 90 grain 30 cal projectile down the 4.6 inch barrel and through the muzzle at over 1,500 fps. This is enough velocity to pierce the brake rotor from a passenger car when using a steel core projectile. Don't ask me how I know. There are plenty of videos on Youtube that demonstrate the penetration abilities of the 7.62x25mm Tokarev cartridge.
To make your case you have moved the goalposts from 2 to 5 grains.
Lots of people hunt deer with pistols.