A heat pump would use way too much electricity. They are also not very efficient when it is cold out.
I suspect a LED bulb would not generate enough heat. An incandescent bulb might. The heat pad that I posted the link to earlier generates about the same amount of heat as two incandescent bulbs would. Better yet though, you could tape or glue it right to the area that froze so it would be in direct contact with the problem area, then insulate over top. If you used a light bulb, the heat would be more point source (pinpoint) and there will be space between it and where you want the heat reducing efficiency (and difficult to insulate).
If your furnace has multiple heat registers, there is a good chance you have a plenum chamber. A Plenum Chamber is simply a sheet metal box that all the duct work attaches to. The heat from the furnace goes into the box and is then distributed to all the ducts. You can probably add another duct to the plenum either via an existing knock-out or by drilling a (large) hole into it. Then run that duct into the space that you want to heat. Of course that space needs to be closed off (insulated if possible too) so the heat doesn't just disappear into space. And you need a reasonably route from your plenum to the area that froze.
You also could simply install a short powered duct (with a fan) from the cabin (preferably a warm spot in the cabin) down to where you need the heat. Then just turn on the fan when you want heat down there. Disadvantage of this and above suggestion is you have to keep your cabin warm (probably 60 or better) to compensate for heat loss.
You also could move the water around, so it doesn't set too long in one place, with a recirculation system. And several of us have discussed (and built) such systems on this forum.
A sneaky way (and what is working well for me now) is an indirect method if your trailer layout allows such. I installed a radiant propane (Wave 6) heater (uses no electricity) in the trailer where it also warms the floor right above the water tank. The floor gets warm (not hot) and heat is conducted down to the tank, the top of which is pressed tightly against the floor. Presto, the tank gets some (not a lot, but it doesn't take much) heat.
One last suggestion but your wife won't like me for it (-:
When I snow camp (in a snow cave or tent), I take my water bottles to bed with me. Usually works well in all but the most demanding conditions (I did have one start to freeze once.....) Of course, I am only talking about two or three 1 liter bottles, not a whole 5 gallon jerry can.....
