Sounds fuel related. I am in upstate NY, and we have different fuel for the winter versus the summer. Fuel needs heat to atomize correctly. During the warmer weather, it atomizes easily. I worked as a mechanic during the 70's (before fuel injection became standard), and that first cold day, there would be a bunch of no starts. That is when any choke problems would show up. We are so accustom to jumping in our daily drivers, and just fire it up and drive away. Carbs were way different. People would say my car is cold blooded meaning it ran terrible in the cold. I see you are in Texas and "we don't need the choke." The colder it is, the more likely the choke could help (cold for me you cold for you may have different definitions). Also on a 68, there should be a heat riser in the passenger side exhaust manifold. It would push hot exhaust gases through the bottom of the intake, so if any fuel didn't atomize, the liquid droplets would instantly vaporize when hitting that warm surface. If the heat riser isn't there or functioning, the fuel going into the cylinder would have large droplets of liquid fuel, that won't burn well, and that in turn could even cause black smoke and run poorly. Up here the fuel is modified to improve atomizing the fuel (even on modern cars) during the winter (they use methane-alcohol-and other chemicals) which reduces emissions during colder weather. In other words, it may just be the nature of the beast. My 68 New Yorker with a Holley (factory carb), the choke would stay on what seemed like forever. Try kicking the choke to stay on a little bit longer and see if that helps?? As far as it starts and then seem to want to stall, that could be because the float bowl isn't filled due to the gas evaporating when the engine is off-and it takes a moment to refill it on the restart.
HTH
