'American Horror Story' Star Ben Woolf -- In Stable Condition ... But Not Out of the Woods

"American Horror Story: Freak Show" star Ben Woolf is no longer in critical condition ... but doctors say he still has a tough road ahead.

Sources close to the actor tell us Ben has yet to wake up ... and is being kept sedated while under constant doctor supervision -- but the upgrade to his condition is good news.

TMZ broke the story ... Woolf was hospitalized after he was struck in the head by a moving car.

Sources tell us his family has been by his bedside the entire time ... and "AHS" creator Ryan Murphy -- as well as other cast and crew from the show -- have sent flowers to his room.