No comma.
facing the door acts as an adverb of manner. It tells
how the clowns stand. You wouldn't use a comma for any other adverb.
The clowns stood straight.
The clowns stood quietly.
The clowns stood facing the door.
facing is a participle. It is the present participle of the verb
face. The clowns were facing the door. Note the similarity between verbs and prepositions: They both take objects.
But, as you say, it acts like a preposition -- although it is not a typical preposition.
They stood near the door.
They stood beside the door.
They stood facing the door.
There are other present participles which are used as prepositions:
Everyone is ready, including me.
I am writing to you regarding the position you advertised.
Harry said all he wanted to say concerning the matter.
So, in summary, I would say that
facing the door is an adverbial participial phrase in your sample sentence.
CJ