I think a little choke theory might help. I apologize in advance, this turned out to longer than I originally intended. If anyone notices any errors, please let me know. When the weather and engine is cold an engine needs extra fuel to be able to start and run, due to a combination of gasoline not atomizing well at lower temperatures, fuel condensing on the walls of the intake manifold, and because cold air is denser and requires more fuel to reach the fuel/air ratio needed to ignite in the engine.
The choke increases the vacuum above the throttle plate, pulling extra fuel from the venturi discharge nozzles.
Early cars had manual chokes, then came the automatic chokes, originally operated by exhaust heat, either from the exhaust manifold or from the exhaust crossover in the intake manifold. A bi-metal spring in the choke housing was warmed by pulling air from around the exhaust manifold or from the intake crossover through the choke housing. These chokes were prone to sticking and required a fair amount of maintenance, due to both exposed linkages and the debris being sucked through the choke mechanism. The electric choke doesn't require heated air to be drawn through the choke housing, thus eliminating one source of problems, by heating the bi-metal spring with an electric heating element. Chokes also bump up the idle speed during the warm up period. The speed that the choke opens up at is self regulated, the colder the atmosphere/engine is the longer it takes for the automatic choke to open. However, all parts must be operating correctly, the proper amount of air being drawn through the exhaust heated ones, and the proper voltage and current being applied to the electric ones. Proper operation must be maintained after the engine is running and warmed up to keep the choke from closing with a warm engine.
After the engine starts less additional fuel is required and the choke butterfly opens a little to decrease the vacuum above the throttle plates. The choke plates opens by one of three ways, the choke plate pivot being offset, a manifold vacuum operated piston, or a manifold vacuum operated diaphragm. Also, to help free up a stuck choke and to have a way to start a flooded engine a mechanical "dechoke" opened the choke plate a little when the throttle plates were fully opened.
Most of the operating parts are exposed and prone to collecting dirt and corrosion, thus still prone to sticking. Many of us still prefer manual chokes, and back in the 60's and 70's manual choke conversions were readily available to eliminate the automatic chokes.