I am freezing characters in place at my game by setting the network owner of their root part to the server. There are plenty of other methods that many of us used to use but this seemed the most logical since the server is the one that wants to keep them in a fixed position.
This did work quite nicely, but after ~6 seconds the player regains ownership and is free to move their character about again.
Of course this means I am not going to use this method to freeze them in place, but it would be nice if it were possible to do so this way.