Not tech, but a good topic.
This is why you should never, EVER, do full throttle runs in weather like that. At least not until all the gearboxes have a chance to warm up. This is completely normal. The viscosity of the oil in the trans and rear end is so thick, and when you warm up your car, the engine oil is the ONLY oil that is warm, you still need to go very easy on her until you've got at least ten miles of continuous driving above about 45 MPH to get the trans a rear diff warmed up as well. This is especially crucial for those people with Automatic transmissions.
Nice, easy accelerations and limiting your speed to around 50 until the oil gets warmed up is what my father, a 30 year mechanic with over 20 of that for GM and six of that in the Navy motor pool as a mechanic, always told me. The most easy way to remember it? If it's in the teens or below, give your car 10-15 solid minutes of steady driving to allow everything to get up to temperature. You'd think it would warm up really fast, but it doesn't when the temps are that cold outside and you're doing 40-50mph, streaming that cold ass air over those components. This is also why you see big rigs with covers over their radiators. If they didn't put those covers on, their diesels wouldn't stay in the optimum operating temperature range while going down the road at 60-70mph.
It would be interesting to see how quickly today's cars warm up the transmissions. Cars sold in the North should come with transmission oil temp gauges standard. But if someone who lives in really cold areas had a temp gauge for their transmission, it would be interesting to see how long it takes a modern day transmission to warm up to full operating temperature.