Ab Snopes burn barns primarily as a means of getting back at those who've slighted him. As a man with virtually nothing—due largely to his own laziness and drunkenness—his campaign of serial arson is his way of exacting revenge on those much wealthier than himself. So, there's definitely an element of class war here. Snopes is at the bottom of the pile, both socially and economically, and those whose property he destroys are much further up. Burning their barns brings them, to a certain extent, down to his level.
Burning barns is also a way for Snopes to make a clean break. Once he's burned down a barn, he gets his family together and ups sticks and moves on to another town. Snopes knows that once he's burned a barn there's no way he can continue to stick around, and that's just how he likes it. He's a man who doesn't like being tied down for any appreciable length of time, and in some funny kind of way, barn burning gives him some measure of freedom.
As for whether or not Snopes's actions are justified, the answer's very simple: they're not. There's no justification whatsoever for carrying out such serious criminal acts. Arson isn't just criminal damage; it also puts people's lives at risk, and there's never a good reason to do that.
Whatever he may think of himself, Snopes isn't some kind of sturdy individualist standing up to the petty rules of society; he's a lazy, ignorant, selfish drunk who treats his family like dirt and has no conception of social responsibility. This makes him a very dangerous man indeed and his criminal actions all the more contemptible.