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we go two foot as a rule of thumb due to tractors, trucks and other heavy equipment. also never know when you may need to dig on top of it for something the pressure say form a large track hoe will break a water pipe only 6" in the ground assuming PVC is the pipe you are using. that is just the way we do it but we have to bushhog so we go 2 ft that is why i suggested that nothing at all to do with freezing pipes as this is what i assume you mean. anyways if none of this applies to you then yes 6" would be fine. and yes if you keep the two trenches seperated by 2 or 3 feet you will be fine.
as for the warm part i wish, we are have an arctic blast right now, not no where near as cold as you but extremly cold for us the windchill will be in the single digits tonight and early tomorrow