This is one of those strip concepts Schulz returns to later. I remember there being a similar strip involving Snoopy, who befriends a snowman, and is heartbroken when it melts away. Cut to Charlie Brown and Linus, who have been watching. Linus: "Poor Snoopy, he's too sensitive." CB: "I notice he's not too sensitive to eat the carrot." I'm paraphrasing, but it happened more or less like that. Even the carrot eating is here, which makes me wonder if that later strip weren't a conscious callback on the part of Schulz.
Anyway, this strip provides a good example of Charlie Brown's developing depression. He really takes this too seriously. I mean, going so far as to beg the sun to stop shining? Wow. A futile statement of man protesting against the universe! I smell a thesis coming on....
As the first panel indicates, snowman building is an artistic statement with Charlie Brown. He's a sculptor who works in the medium of snow, and he's at least got Schroeder's admiration for it.
I wonder if this isn't some kind of statement, conscious or not, by Charles Schulz about the ephemeralness of his own medium? Peanuts will probably be around much longer than other concluded strips, mind you. There are a lot of forgotten newspaper comics out there.