In my opinion, the major instance of irony in this story is the situational irony that comes at the end of the story. Situational irony can be defined as a disconnect between what you would expect and what actually happens. To me, the ending definitely fits this definition.
As the story draws to a close, I (at least) expect that the two men have resolved their conflict and will become friends. I assume that someone will find them and get the tree off of them. This assumption sets up the irony at the end. Instead of being found and saved and becoming friends, the two men are found by wolves and are presumably going to be eaten.
So the ending takes my expectations and turns them on their head -- situational irony.