It strikes me that, right now, we are about halfway between the original look for Peanuts and the "classic" style of the strip's heyday. Charlie Brown still has an oval head and solid black eyes, but his proportions are a bit less stylized. Snoopy is still relatively small compared to the other characters, but he is a bit longer. (He's still far away from the balloon animal-like look he had in Peanut's later years.)
Oh, the strip itself? There have not been a huge number of funny-cause-he's-a-dog strips so far. (The one with the TV antenna atop his doghouse has been the funniest of that lot.) Thing is, as Snoopy's personality becomes better-known and he becomes less like a normal dog, these kinds of jokes become less effective. I remember, as a kid, seeing some old compilations of Peanuts strips with Snoopy jokes and not quite "getting" them because the humor was tied up in Snoopy doing non-doglike things, when most of my experience with the character came from the days when he had almost given up dogliness altogether.
Just today I saw a copy of one of the old Fawcett Peanuts collections, flipped through it, and found the strip in which Sally laments that she can't go to school because she's not old enough. Snoopy responds in a thought-balloon that you also have to prove you're a human. I remember that strip from reading it in 1st grade and not finding it especially funny. I like it a lot better now.