No, you want the plane to be a clean and slippery as possible to the incoming wind. Controls, especially on small planes, are locked in a neutral position so they do not allow the wind to catch any of the control surfaces. You then tie the plane down in at least three locations. Most parking spots have one for each wind and one for the tail. This is usually enough to secure most planes in most conditions. Stuff outside the norm though could break a tiedown or buck a plane around enough it could damage a control surface or break the tiedown point. I've seen it happen when someone didn't tie down their plane well enough. It was jerking around going from loose to taught on the ropes until one of them gave way and it flipped over.

A nose down position or trim would create lift on the rear of the plane allowing for the possibility the tail could lift damaging the aircraft.