Bob,
I have been thru quite a few as well. I always parked whatever I had at the time on the side of my house opposite whichever way the wind was coming in. When we built our new house I now put it away from trees along the yard but keep it under the shelter. I did not put ends on my shelter due to the chance of hurricanes and such. My shelter is 42 foot by 40 foot and 20 feet high and ends would give it the "umbrella" effect.
I never put the stabilizers down to directly answer your question. We pull or drive them down the road at 65 to 80 mph depending on how heavy your foot is so it will not blow to pieces. Trees, flying debris is another subject though. Position it the best you can away from flying projectiles and stay safe. We are looking for 70 to 80 mph up here.
Again stay safe and God bless.