First, welcome to OCC..........
You can safely move a Cub Cadet Tractor with a Hydro Transmission. The early model had manual Relief Valves, that a lever needed to be lifted up to release internal pressure, before the move could be done. Later models, had automatic Relief Valves, where once the motor stopped, the internal pressure was released. Note, that a lot of the older manual Relief Valves were updated to the newer automatic type, regardless of tractor age.
Either way, once the internal pressure was gone, one could move the tractor with out issue. Moving the tractor for a mile, at 25 MPH, would be a "no-no".