The three conflicts in "The Law of Life" are the following: man vs. himself (or, more specifically, body vs. mind), man vs. man (or, more specifically, father vs. son), and man vs. nature (or, more specifically, man vs. snow) in that exact order.
First, there can be no doubt that the main conflict is man vs. man. Koskoosh's old and withering body is conflicting with his mind's desire to stay alive. Koskoosh spends the entire story continuing to value his life as he is left to die in the snow (just as Koskoosh had left his OWN father to die in the snow).
It is well. I am as a last year's leaf, clinging lightly to the stem. The first breath that blows, and I fall. My voice is become like an old woman's. My eyes no longer show me the way of my feet, and my feet are heavy, and I am tired. It is well.
In regards to man vs. man, we can't deny (as readers) that SOMEONE has left Koskoosh out to die. That man just happens to be his son. Even though Koskoosh's son is simply following the tribe's protocol to leave "useless" beings out to die in order not to become a public charge, a reader can't deny that this pits son against father.
Finally, we have the minor conflict of man vs. nature. There is no doubt that Koskoosh is fighting to stay alive despite the exposure to the elements (in this case, freezing cold weather). Koskoosh's elderly age was not enough to cause death (despite the conflict in his mind). Simply banishing Koskoosh was not enough (despite the son's goal to do so). It is NATURE that actually accomplishes the task. A human body simply cannot survive cold without adequate clothes and shelter. Therefore, we can't negate this last, important, conflict.