Depends on how cold it gets where you are in Missouri.
In our area, North Central B.C. frost goes down at least four feet, in an area that is not walked or driven on.
As a rule, we bury water lines at eight feet, or deeper, with 2" styrofoam over it if going under a driveway.
The line is more susceptible to freezing for the first few years, until the dirt settles in.