Not really, the ground can freeze and get colder. This is why early winter, first snow and flurries will seem to melt instantly when they touched down, but as the season continues the ground cools off till snow can stay frozen on the surface.

While it’s true the deeper you go the more stable it becomes, the earth has thermal layers just like the atmosphere, and whats more the water above the ground insulates the ground from freezing faster, so the deeper the water the less it’s going to freeze from below.