You could, but here is why you shouldn't.
Your truck has a DPF (the soot filter for the emission rules). At idle or high idle (1000rpm) in those temperatures it will fill up fairly quickly and go into re-gen mode which uses a lot of fuel to burn it clean again, this process will happen several times a night while you do this, fuel is not that cheap. Your engine will also be running cool, the temp gauge may show it is warm but a lot of things inside your engine will not be including your oil. This can lead to condensation build up which attaches itself to the sulfur in your oil (combustion by-product) and creates sulphuric acid, not real good for bearings. There are a host of other reasons why it's a bad deal.
If you are going run in the cold regularly it would pay huge dividends to you to buy a diesel fired heater (Espar or Webasto). The payback will be very quick in fuel saved alone!
How do you like the new DT10 motor?