A wise man once said you can't teach an old habit new tricks before it dies hard. Or something along those lines. In the early days of the automobile, owners did well to get their cars running after a dozen attempts, and keep it running for as many minutes -- and that was on the best of days. Times have changed quite a bit since then, and so have the ways we maintain and drive our cars.
Back when even the best cars on the road ran on metered fuel leaks -- aka "carburetors" -- automobiles had a difficult time running while cold. Engines are designed to run at a certain temperature, usually around the boiling point of water. Much above or below that temperature, and the engine loses combustion efficiency and fails to turn the fuel going in into horsepower. Carburetors got around this problem using a choke, which limited airflow and proportionately increased the amount of fuel in the mix. The choke had to stay closed until the car warmed up and combustion efficiency came back up to level. By that time, the engine's metal had expanded to where it needed to be, and all the fluids were warm and circulating. Unfortunately, carbureted cars were often so cantankerous during the warm-up period that they were all but undriveable for several minutes -- hence, the need for a considerable warm-up period before setting off.
Prior to catalytic converters, few people really thought about warm-up procedures provided that the car eventually warmed up while idling. However, things changed drastically from the factory perspective when cats debuted. A catalytic converter works like a chemically enhanced furnace, burning off unburned fuel before it escapes from the exhaust pipe. To do that, the converter matrix has to reach a certain temperature -- usually about 800 degrees Fahrenheit. This "light-off" took a long time on carbureted cars, because the presence of extra fuel in the mix via the choke lowered combustion temperature, which ironically made the converter take that much longer to light off. Over a few years of raw fuel pouring through for several minutes without light-off, impurities in the fuel would clog and "poison" the converter.
Things changed drastically after the introduction of electronic fuel injection, and even more after 1996 when the government mandated that manufacturers start paying attention to converter light-off times. Electronic fuel injection allowed engineers to run the engine on several different programs, and change fuel injection timing and the air-fuel ratio for the engine and operating conditions. This further allowed for the fine-tuning of start-up programs specifically designed to light the converter off very quickly; these days, 20 seconds or less isn't uncommon from a dead cold start. Modern cars also typically use multiviscosity oils that get parts slippery far more quickly than the old single-weight oils, and those oils tend to do a better job of sticking to parts after the engine shuts down.
With any modern car, your warm-up time at idle should be 30 seconds or less; most cars these days are designed with minimal warm-up times in mind. So, give your car 30 seconds under most circumstances, perhaps as much as a minute if you're starting out with 0 degree temperatures, and then slowly set off. Drive easily for the first few miles to give your transmission, drivetrain and suspension components time to come up to temperature. It's a myth that idling is the best way to warm a car anyway. Engines produce more heat under load, so the quickest way to get your engine up to temperature -- and your heater working, if need be -- is to drive the car. That goes for cat light-off too; the converter will light off more quickly while the engine is under load than it will when idling. Try running your own test some time. Record how long it takes your engine to reach operating temperature from dead cold after a 30-second warm-up and gentle drive, vs just leaving it idling in your driveway.
