It will take a quite strong wind to move a deck; it is relatively heavy, has a low center of gravity, and has comparatively little surface area exposed to the wind. Frankly, I suspect you'd be more likely to have a travel trailer or fifth wheel trailer blow over (particularly if the wind is from the side) than most decks move significantly.
You can get anchors for animal tethers that are like large corkscrews at feed/farm supply sorts of stores, and attach the deck with cables or whatever to them. A few of them would ensure that the deck stayed in position regardless. You should, of course, verify with the management that they would be permitted, which probably depends somewhat on their main concerns. These anchors don't leave objectionable holes in the ground or harm the grass etc. much, but they could wreck havoc with utilities that are close to the ground.