A cleaning designation or cleaning activity zone would be better than this idea as far as cleaning stuff up. a cleaning zone would probably include inside/outside/zone-only/anwhere options. Control over job priorities is suggested elsewhere as well.
HOWEVER, a burrow to make dwarves think an area is inside the fort?
That's a splendid idea!
"Urist mcdrenched cancels sleep: throwing tantrum".
On inspection of thoughts: "has complained loudly about the leaky roof", "sleep interrupted by weather", "complained about the cold room", and topped off by "complained about the draftyness of the room". Maybe tricking your dwarf into living like an elf wasn't such a good idea...but if you really had no choice but to sleep under the stars (big aquifer, mason used up all the building materials except a couple planks to make a statue), you could at least make sure your dwarves appreciate sleeping next to the artifact statue.
It would require a number of secondary reworks to get the balance right, most of which go best with improved farming. but I do think that a dwarf will expect certain things if they're in a room, and will hate getting wet if they go to sleep in a bed, but will only dislike getting wet if they plopped themsleves down on a patch of dirt.
Again, if there are aquifers everywhere, it can still make the difference between if there's only one section of the map that's not about to be hit by a boiling blood rain and there are aquifers everywhere you look.