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.
Below the frost level and protected by Insulation (rigid type) and even deeper if heavy traffic drives over it or heavy animals walk above it (cows , horses...) heavy animals will drive the frost down as much as 8ft. or more in the right conditions. Been there done that! Solid ice in winter that the backhoe could not break thru to get it repaired.