I was going to comment in reply to NKCampbell, pointing out that as well as walking on two legs, putting clothes on himself, ice skating, and typing letters to his brother, Snoopy is also a famous World War I fighter ace, when I noticed the reference comic in that link demonstrates that Linus at least understands what's going on in Snoopy's head, even if he doesn't have a direct translation of individual thoughts. (He shoots down Snoopy from his Sopwith Camel/kennel.)
Additionally, that page suggests Marcie understands Snoopy's thoughts inasmuch as she is happy to play the French lass who falls for the hero in his fighter ace fantasy
Edit: Further instances of the characters being aware of what Snoopy is thinking:
Charlie knows Snoopy has just bailed out of his 'plane'
Charlie knows Snoopy is flying a sopwith camel in world war 1 against the red baron
The example below is wrong. It is Woodstock talking. I couldn't see him in the image (still can't), but it's his speech. Thanks to @DaveTweed for the correction. I still think there is enough evidence to show there is definitely some understanding of Snoopy's thoughts by the Peanuts children.
Evidence of direct understanding of Snoopy's 'speech' (not thought) bubble:
So yes, Snoopy
iscan be understood by the human characters in the strip.
Edit 3: To respond to essentially similar comments from RDFozz and cann-ned_food:
For the first part of the argument, I suggest that for a strip that started in 1950, realising that Snoopy is a World war 1 fighter ace is NOT an obvious reaction to seeing him dressed in aviator hat/goggles piloting his kennel. A 1950s pilot would be more likely than a WWI
pilotfighter ace, (heck even a WWII pilot would be more likely).
For the second, the logical end result - once you start down the path of assigning parts of the strip to someone's imagination - is that the whole thing must be imagination based, whether that imagination is Snoopy's, Charlie Brown's (whether or not that includes the rest of the Peanuts kids) or that of Mr Schulz himself. I felt this would invalidate the question, so I chose to not only not go down that path, but to ignore it completely.