Cancelled by A&E in 2014, Longmire was picked up by Netflix for the fourth season.
The funeral scene was filmed at St. Paul's Episcopal Church in Las Vegas, New Mexico. This was identified by the stained glass window where Walt is standing. (And by the sign outside the church.)
As the superstition goes, a cowboy hat should be stored with the opening facing up, so as to "catch luck" inside of it. Alternatively, laying a hat with the opening down allows all the luck to fall out. Walt first places Branch's hat brim up at the funeral and then, knowing the circumstances, turns it brim down.
Before telling Cady about Branch, Ferg says "Shit" as he prepares to deliver the news. This is the first time in the series someone besides Vic has said the word.
When Henry is returning the defense money, he talks about people leaving notes for Hector at the wall, he points toward the wall with pursed lips, which is a very Native American thing to do. It is very common among the Navajo.