Possibly, but the salt allows water temperatures to exist lower than 32. Unsalted water almost always freezes right at 32F (possible to supercool but you wouldn’t be able to agitate it or put anything in it).
Adding dry ice to water just makes ice, the water can’t get any cooler than 32.
Ocean level saltwater (5% salt) freezes at 28F. A completely saturated salt solution (20% salt) freezes at 2F. I don’t know if I want fully saturated but maybe a little saltier than ocean water is in order.