In NJ, I would think a heated water hose is only going to be one of your considerations. Addressing the livability and comfortability issues may take most of your time and planning. You don't state how many folks are going to be living in the 5'er but that would bear on the situation. Having two teenagers can tax even a residential water and sewer system.
There is a full-timers section on this Forum and I'd bet there are some folks living in the climes like NJ that have a lot of good ideas about how to make it through a few months. You may wish to start a thread in that section.
For making things comfortable, there really isn't anything above the installation of skirting. Skirting will help keep the floor from getting cold in Winter weather, especially if you can run either auxiliary heating in that space or use heat lamps. One of the best skirting materials is straw bales as the dimensions are big, i.e. best R-value, and can be easily disposed of later. If using bales, it would be a good thing to install a barrier between the bales and the underside of the trailer. That will tend to keep wandering critters from Wintering-over underneath or in your rig. Mouse traps are a good deterrent with any skirting.
An alternative is to use foam board insulation and plastic film. With foam board, you can fashion containments to enclose dump valves, water entrances, and even run it up the sidewalls for additional thermal breakage. It may be possible to use the foam board after your encampment to insulate spaces in your house. That would mitigate costs.
Good luck on your stay in the 5'er. Keep us posted on how that worked out.