Absolutely, just warming up the engine does not do anything for the rest of the drive train. The transmission, differential, wheel bearings, power steering, tires, etc. will still be stone cold until you drive some distance. I would definitely take it easy for a couple of miles in cold weather.
Driving a car in winter is like aerobics, take it easy initially. I used to live just two blocks off the freeway, and in the morning I would stay in the slow lane for 5 miles or so, before getting up to the legal speed limit.
The transmission, differential, wheel bearings, power steering, tires, etc. will still be stone cold until you drive some distance.
Ah yes, the horrible memories are returning! Day after December finals in Troy, NY and I’m heading home. VW Beetle with straight 40W oil in the crankcase. -20F. I had to have a bunch of people push start me the night before, so I parked on a steep downhill street, ready for the roll start I knew I would need to do. Got in, key on (start attempt was a single “wrr”). Released parking brake. Nada. The wheel bearing grease was so stiff the car wouldn’t even roll down a steep hill! I had to round up a bunch of passer-bys to push me downhill until the Bug was rolling on its own. Fortunately the roll start worked. I didn’t dare turn off the engine all day, until I was 300 miles and home.
When it’s super cold, an engine does need to be briefly warmed up until it’s idling smoothly. Most cars don’t need any warmup (just gentle driving for a while) in any weather warmer than that. If you need the defroster going immediately, that could require additional warmup time. The heat will come up faster if the car is being driven than if it’s idling (and you’ll get non-zero mileage). Most of the time, it’s just a waste of gas to leave the car idling to warm it up (also a theft hazard). If it’s chronically cold where you are, consider a garage or an electric block heater.