Lots of spoilers in this thread. Don't even bother if you haven't seen it.

The film reminded me of Tintin's "The Castafiore Emerald", a story full of clues and leads that ends in nothing, because the author wanted it. But here the director/writer wants US to solve the crime, and here's my take.

We have forgotten an important moment in the movie: When the fat babysitter tells the mother "I know a good medium, she can help you", she is suggesting she can give her the name of the killer, i.e., clean herself. Why? She and the mother probably have an affair (why not? This is a severe case of cabin fever). Who was the woman she cheated on him with? Well, that's pretty clear to me. Also, the kid washed the dog BEFORE a walk in the snow. Don't you think that's suspicious? Maybe he didn't want to do it and then he was forced to do it so "not to see something horrible that may happen but it has to happen". The father was the fifth wheel in that family, and since the mother was already having fun with the sitter and the kid approved, well, he had to go. We never found the murder weapon because, alas, the sitter took it and threw it in the snow. The sitter was NEVER brought to court, that is, the mother was trying to protect her. But she was there a few hours after the fall.

In a nutshell: The mother approved the murder commited after the stupid hubbie didn't want to stop the PIMP cover blasting off the speaker. The sitter did it, and she sent the kid out with the dog so he is not a direct witness.