Not sure I understand the original question. Do you mean 'insulate' these areas to keep the hot water
hotter or from freezing while in use? I have never heard of anyone adding insulation to the water heater area for this purpose... or any other for that matter. To be honest, I'd be concerned about the possibility of creating a fire hazard. Further, heat inside your trailer, and the fact that the water heater will be lit, should be all it takes to keep these areas from freezing while in use.
To answer your second question.... yes and no.
IMO, it's much easier to winterize the trailer's plumbing and simply not use it at all during the cold months. Beats having to re-winterize after every trip. Instead, pack a few gallon jugs of drinking water and bring a porta-potty. Unless you're camping for more than a weekend, shower before you leave home and put it off until you return. Rinse water, such as for brushing teeth, can be collected in a cup and disposed of in your porta potty.
You'll also save from using the water pump, thereby conserving battery power.