The internal conflict in this short story is the disposition of the two lead protagonists and the way that they let their deep-seated rancour fill them and cloud their reason. The introduction to this short story makes it clear that this disagreement is one that has been inherited down through the generations of the two different families and it is one that both characters are obsessed with:
...the dispossessed party hadnever acquiesced in the judgment of the courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations. The neighbour feud had grown into a personal one since Ulrich ad come to be head of his family...
It is this feud that causes both characters to be out on such a dark night and it is this feud that leads them into the sticky situation they find themselves in. In many ways, it is their own internal conflict within themselves and their inability to forget and forgive that is more powerful than any external forces, at least until they meet during the course of the story.
The external conflict is provided through the conflict between the Znaeym and von Gradwitz families, but also the conflict between man and nature. The way that a tree falls on them both, crushing them together, and the rather unfortunate ending of the story makes it clear that nature is a far bigger source of potential problems for these two characters, and ultimately results in the downfall of them both.