Flushing the cooling system on the trailer with muffs isn't much different than running the boat in the water, assuming you don't have a closed heat exchanger system. If your boat doesn't have a cooling issue, high or low temp, don't worry about it until you have it back on the trailer and winterize it. If you have a closed, heat exchanger system, it gets more complicated, and someone else can chime in. If not, put on the garden hose muffs and run it until it comes to normal temp. If you need to winterize it (if it freezes where you live, you do), and do it yourself, remove the exhaust manifold drain plugs, the hose from the engine water pump, the water supply hose from the power steering cooler, and the engine block drain plugs (unless you have that heat exchanger). Make sure the engine plugs drain freely. Sand and junk can plug these, so give them a pole with a nail or small screw driver if they don't really pee out a lot of water.
Steering looseness can occur in several places. A quick, easy check is to tighten the two bolts at the top of the gimbal ring. You'll have to turn the steering hard each way to get a back up wrench on the nuts. 55 ft. lbs. of torque.
Try changing the nav. light bulb(s) as advised above.