Although we only occassionally have such weather here in southeast Kentucky as described by the OP, when we do it's not much different than what you are experiencing in Indianiapolis.
My #1 aid is one gallon jugs of hot water (about 120F-130F). I use it sparely working on the parts (top of door jam down the sides to the handle, etc.). Yes, I do dump it on the windshield...........haven't cracked one yet!
Once I get the driver's door open, I start the car and put the heat system on defrost with the fan on low................then I let the darn thing idle. That's all a bunch of bull$hit that your TDI engine is being destroyed by letting it idle.
Case in point 1: In the winter of 2003-04, I was TRAPPED in a traffic back-up on I-75 for over 6 hours......snow, blowing snow, and 23F. My car idled the entire time.
Case in point 2: On cold mornings if my wife is riding with me, I start the engine and let it idle as much as 15 to 20 minutes.
Case in point 3: We love to rumble thru yard sales. Each year there is a yard sale on Highway 127 from Chattanoga to Cincinnati in the month of August. We take in about 100 miles of it each year....... With the AC on, I never shut-off the engine!
Now at 280k miles and running strong.......... is my engine in trouble? I seriously doubt it!
Rest my case!