I lived in Anchorage for 20 years without a garage. I had a Tercel for 17 of those years (only sold it because we moved).
If the temps were around 10°F, I'd plug my block heater in and then turn it on at my switched outlet while I made my morning coffee and let that work for an hour.
Otherwise, I'd just crank it and ease out of my subdivision. I'd take it slow the first half mile or so, but nothing special.
I've read that excessive idling can clog up a catalytic converter, but mostly it was my experience that my cars would warm up faster if I just got in them and drove off. A block heater warms the oil and helps the engine start, and can help with emission issues, but I don't think it has much affect on the transmission or other cold parts.
For really frosty days, I had an auxiliary dash heater that I'd use to clear the windshield.