As long as you are moving, the water probably will not freeze. When you stop, if you have a heated, enclosed underbelly or tank heaters the heat will probably keep the water from freezing as long as you open the doors to the water lines inside the trailer. At least, that's my thoughts, for what they are worth.
2012 GMC 2500HD D/A Crewcab
2012 Jayco Eagle SuperLite HT 26.5 RLS
2009 Crestliner Superhawk 1900
2013 Polaris Sportsman 550 EXP
2008 Polaris Sportsman 700 X2