Up here, we let our vehicles warm up a bit before taking off only when it gets cold. Metal and plastic starts to get brittle in cold temps. As for today's vehicles and oil, it may not be required to let it warm up, but it doesn't hurt any.
Back in the day, I lost a 92 suzuki sidekick cam gear and cam at -32, starting and driving cold then accellerating without letting it warm up.
Didn't make it to the end of the driveway. Just cracked it.
I've also had to replace the front hood bug deflector last winter. -41 and I had to boost my truck, I just touched the hood deflector plastic to open the hood, and it shattered. Stuff gets way to brittle when cold.
Another thing that I do in the winter, (and this may be another old wifes tale), is that I back my trucks into it's overnight parking space when the truck and tranny are at operating temps at night. So that in the morning when the tranny is cold, it doesn't have to be put into reverse, just put it in drive and go. I started to do this a few years back when I got the Jimmy. Something about with the 4.3 tranny's, many are blown when put into reverse when it's very cold. Thick cold fluid puts excess pressures on a small valve or something like that? The reverse valve is smaller /thinner and more suceptable to damage then the drive valve? IDK, but it's easy to back in when the tranny is warm just to be sure.
Even if it's not required to let it warm up, can't be a problem if you do. Remote car starters are a hit every winter up here, and after I lost one engine, I'm not keen on loosing my new crate motor. I have a rule, when it's -20 or lower change longjongs from thermal to fleece, and let the trucks warm up!
BTW, thermal longjongs go on after September Labour day long weekend, and come off on May two four long weekend, about the same with letting the trucks warm up.