Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Limited Omniscient)
There is no "I" in snow, and the person telling the story is clearly a narrator who isn't involved in the action, so right there, we know we're dealing with a Third Person point of view. But is it objective, omniscient, or limited omniscient? Let's dig a little deeper with our snow shovels.
To be objective, we'd need to be hearing from someone who offers us no insight whatsoever into what characters are thinking or feeling. We know that's not the case when we hear a few of Peter's internal thoughts. He thinks it would be fun to join the snowball fight, but he knows he's not old enough yet (23). And later, when his snowball melts, we learn that Peter "felt very sad" (32). Those two instances let us know that we're dealing with an omniscient narrator, but since those are the only two instances, and since they're limited to just one character, we can arrive at Limited Omniscient.
Hm. If only someone could have let us know how that snowball felt…