18 inches is code, or 12" with 2" of concrete on top.How far off is your shed? You can run a single underground-rated romex line out there buried a foot deep, as long as its fed by a GFI. It's so nice having power in out-buildings.
My blowers crank hard near zero, but thankfully I don't get snow in a weather pattern that brings that kind of cold. Usually. I run whatever junk leftover synthetic in them, 5- or 10w30.
If you run it in conduit you have to de-rate it 10% and use individual strands of wet rated wire as conduit is never considered to be a dry environment.
Not saying you HAVE to do that, just providing the info in case they didn't know