Yeah, after watching one episode this season, you also get a feel for what Mathias has to deal with in his police force. I don't know if what he was telling Walker was true or not....that they only have the power to deal with "misdemeanors".
Hopefully, this isn't giving too much away:
Their power seems only provisional, and they are obviously (and understandably) resentful of it....witness their reaction when Cady Longmire came into the station. They only have the power to deal with "misdemeanors", if Mathias was not lying to Walker.
And they're very protective over their jurisdiction, which seems to be about all the power they truly are allowed to exercise.
I'll forgo further speculation about Nighthorse, as it could involve potential spoilers.