Depending on your location and how cold it gets in your area water pipes need to be buried between 4 feet to 6 feet deep.
However in some locations where it gets really freezing the water pipes need to be buried as deep as 7 to 8 feet deep.
The deeper the water pipes are buried the less risk they have at freezing because the ground below the earth is warm compared to the ground above.
Check with your local area about the frost line but if you bury the water pipes at least 5 to 6 feet deep you should be okay.
It would be better to bury the water pipes in the ground deeper than required to prevent frozen pipes than it would to bury them to shallow and have to deal with frozen pipes.