Thanks for the input.
3 to 4 amps is around 40 watts of power at 12 volts. That probably is not enough heat to really do much in a short cycle no matter how hot the solenoid magnets feel.
As to energizing the brake solenoids...
I'm not suggesting that the brake solenoids be left on continuously. My thinking was more along the lines of energizing them for a period of time to help to drive moisture out.
I don't know the duty cycle of the solenoids. It seems to me that it would be a poor design for them to have such a short duty cycle that they would burn out in the short term. They can see a bunch of heat when being called upon to operate on long downhill grades.
Perhaps it is a hare brained idea, but it is an idea. That is why I posed the questions.
I already purposely use the manual electric brake switch when I first test tow the trailer around our local streets in the Spring. I drag the brakes at slower speed for a time for a couple reasons.
It assures me that the brakes are working.
It helps to wear off some of the rust on the drums.
It heats up the hubs a bit so that I can feel for temperature. That gives a half-***** simple test to see if all brakes are operating. If one hub remains cold after my slow drag procedure it may indicate that the brake on that wheel isn't functioning.
Some further more sophisticated tests are here.
I feel that my short slower speed local test towing also allows the flat spots on the tires from storage to more gently work themselves out. I have no data.