Tarps are fine in any temp, essentially all tents are is tarps stitched together.

I spent MANY a night is 30-40 below or more in nothing but a tarp and ground sheet.

The key is insulate the ground under with spruce boughs at least foot or more thick.

String the tarp like a teepee with the centre strung up. Pin the sides down tight and seal with snow or logs.

Condensation will form and freeze, not a big deal to scrape off in the morning.

You need a large tarp to do the teeppee style setup but the key is limit the interior space to a minimum thus less airspace to heat up. A candle lantern does well to keep the chill out.

Keeping wind out 100% and ground insulation is the goal as it dont matter what your bag rating if those 2 arent taken care of.

Hound