You are right that any flat tarp is not going to work in heavy snow fall. The simple solution is to pitch the tarps down in the center; in other words, pitch your tarps just as you would normally.
If everyone had triangle tarps, you could use a tall pole in the center to create a pyramid tarp. I suppose if each were customized with Omni tape on the edges you could seal up the peak. I suppose that might be a customized tarp: triangle with Omni tape on inner side and hex on outer side.