For ice blocks or cubes, not really. If you read the section on commercial icemakers, making ice at lower temperatures causes impurities to be trapped. If the ice is subcooled at a later stage it's ok, but then the process is more complicated. read more
You can make water ice as cold as dry ice, sure. You just need a really cold freezer (or alternately, you can pack water ice with a bunch of dry ice, and that will cool it right down. But the water ice won't stay that temperature. read more
We can do a thought experiment. Consider an adiabatic reactor at 1 atm ( volume can vary). Let the volume of water initially at 0C be V_w, and the volume of dry ice be V_i=V_w cc. Take the density of dry ice to be rho_i=1.5 g/cc and the density of water rho_w=1gm/cc. Now the heat of sublimation of dry ice at 1 atm and 25C is 571J/gm. read more