This is a constant matter of discussion up here in Alaska. When I was growing up, our cars were carbureted, so they would literally barely run when it was cold enough- you could put it into gear and it would likely stall. Since then, fuel injection happened, and cars are much better at running when cold.
Reading through the owners manual of my OG SAAB 900 really informed my current practice- start the car, let it idle while I scrape frost and ice off the windows if needed, and then drive pretty mildly until the car is up to temp. While wear is increased when the engine is run cold, the way to maximize the revolutions your car engine turns at cold temperatures is to let it idle. I'm a big fan of plugging in the block heater if it is 20° F or colder- this helps it come up to temp much quicker. Even better is to get a garage. A good quality synthetic oil can help reduce wear as well. If it is really cold, and you didn't plug your car in, yeah, I can see the advantage of letting it warm up a bit if it wants to stall or the HVAC system can't keep the windows clear.
That being said, there are still plenty of folks that insist on using auto start devices. While hopping into a warm car is admittedly more pleasant, you can smell a city of idling SUVs up here on cold days. Its better for your car, your wallet, and the environment to keep idling when cold to a minimum.