waitwaitwait! I've seen a "toilet like facility" in that cave you come by on your way to Riverwood. (small wodden steps going up on the right from the road you can take while traveling to riverwood the first time).
MINISPOILER !
The entrance is guarded by one bandit, there's a rock trap at the begining and two more bandits talking about said guard and rock trap and how "invulnerable" their cave is because of this security system

)
When venturing further dorn the cave you'll get to a room with a furnace and blacksmithing tools eventually. If you instantly turn right, you'll pass a small stall of sorts (without a door though but with a single bucket standing in it)...
It was the only "facility" I've discovered so far but I doubt that this is the only place all of skyrim meets to take a dump.. should be a hell of a line in the morning... on the other hand - that reminds me of a few LARP festivals though ;D)