Years ago when I took the Coast Guard Auxiliary course on Boating Safety, the instructor taught that we should never put the trailer in the water with hot bearings. He said that when the bearings are submerged in water hot, a vacuum is created that sucks water into them. I don't know if this is true but I always took his advice and while I'd let the bearings cool down I'd repack them with my grease gun figuring that if they were full of grease, water couldn't get in.
Of course the main reason for waiting a while to put in was to open all the hatches, windows, doors and whatnot to let the fuel fumes dissipate before starting the engine. Since fuel fumes are heavier than air they settle in the lowest part of the boat. I had an I/O at the time, I've never had an outboard so I don't know if that's necessary with one.
He also recommended unplugging the trailer lights before putting in.