Mimi doesn't put a ring on Steve's finger.
Just after mid way of the show, it is implied that Mimi's mother can smell the corpse through the coffin and tarp, however it has been established earlier that it is cold enough outside to freeze the ground solid and they moved the coffin to keep it from freezing to the ground before heading inside. Additionally, anyone familiar with bridges and ice, knows things freeze faster when in contact with cold air all around. Therefore, the corpse should be frozen solid and no smell discernible, especially after being prepared by a funeral home for burial as alluded by Drew's mom.