This discussion may contain spoilers!
I've played the game three times now, and I'm pretty sure that the Red Haired Men is not the killer.
I don't know if someone brought it up before, but here's what I think (and what will happen in the next four eps). In the first episode, Bigby says that Faith was killed with a weapon that has Magic attached to it - and, as we find out later, Woodsman's axe was blessed by druids. But he's NOT a killer - even though some people may think he is. Here's where Dee and Dum come into play - Dee says that he is a private investigator for someone and has a few questions for the Woodsman - I believe he's telling the truth and that he's working for Faith's pimp! Think about it - one of his girls is dead and he wants to find out who killed her, so he hires two investigators to follow two obvious leads - that's why they were searching Woodsman's apartment (for the axe) and Prince Lawrence's apartment (pimp might have thought that he was jealous of faith and probably killed her with some magical object). OK, but what about the Red Haired Man? Of course, he was at the crime scene, but also in many places which were SOMEHOW investigated by Bigby. Question - how would he know where to look for him?
Here's my theory (based not just upon the gamplay, but also previews of the episodes in main menu and the comics) - someone is trying to take over Fabletown, so he starts with the murder of Faith - because, obviously, the first three investigation paths are husband, pimp and the last client (with Woodsman being the easiest to frame, since he might be in the possession of murder weapon). Bigby, for all his willingness to be better, is easy to be provoked - the Red Haired Man is hired by someone to follow him and make sure he disobeys Fabletown's law (so Bigby can be removed from his position; besides, this person - judging from the game files - is The Boy Who Cried Wolf, so his name is fitting to the situation). It doesn't work out, so the murderer targets Snow, as this may easily push Bigby off the edge. My guess is that Bluebeard is orchestrating this, even though he is not a killer (he is seen in episode three or four as taking Snow's or Crane's positions) - he doesn't want to get his hands dirty, just like in comics, where he is always indirectly involved in something. I think that later on Bigby will be implicated somehow for the murders and become fugitive, so he will have to find the killer on his own (but unable to take down Bluebeard, as he is fine in the comics) to clear his name. Snow will probably be ressurected somehow. This will also explain why her attitude became colder in the comics (because she was 'killed' by a Fable after all, so she won't be that nice anymore) and Bigby's obsession to arrest Bluebeard anytime, without any real reason.
What do you think?
EDIT: IF it turns out that Bigby will be accused, his enemies may have a strong evidence - after all, how hard is it to tear off someone's head if you already tore off Gren's arm?