The legality of use relies on the good neighbor part,
If the field is farm land (farmers get equipment in some how) you can find the owner and ask permission. County assessor websites sometimes have maps with lot searches that will give you an owners name, otherwise it's just asking around.
If it's city, county, state land then it may be a no permission no way.
That said so long as it fits between the posts drop the chain link mesh, roll it up out of the way, pull the top rail, and back it in with the truck
The other option I see is to bring it in head (tongue) first, spin it, and back it onto the pad.
That is where you may need to pull a fence panel (not sure which one) to gain some tail swing room, but I bet if you start bringing the tongue over gradually and hug the AC unit the tracking physics of a trailer will let you make the swing into the yard w/o taking the fence out.