maybe if you could describe your composting setup a little. Is it an
outhouse? Is it up in the air so there's freezing air going underneath it? Is it inside but the tube is exiting an exterior wall and freezing at that point?
I'm guessing, since you are asking the question, that heavy insulation wouldn't work? The ground is frozen so there's no help in burying it?
Using only 45 degree angle turns in the line, this might be a bit labor intensive, but if it's outside, building a working
compost pile over the tube (protected by metal pipe that can withstand 180+ F temps) and keeping the pile warm, if not hot, would be a passive kind of heat. But you'd have to have a big supply of easily-composted carbons stored up. Maybe sawdust kept damp with urine.
An important distinction: Permaculture is not the same kind of gardening as organic gardening.
Mediterranean climate hugel trenches, fabuluous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.