It depends on how you define a character, but yes.
Snoopy conversed with Woodstock with thought bubbles, as evidenced by this passage from the book "My Life with Charlie Brown", by C. Schulz.
I would much prefer that Snoopy not converse with Woodstock, but there are some ideas too important to abandon, so I have him speaking to Woodstock through "thought" balloons.
So Snoopy is not actually speaking, but using thought balloons that Woodstock understands, so there is at least one recurring character in Snoopy that understands what he is thinking.
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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 Edit 2: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.
And finally: Evidence of direct understanding of Snoopy's 'speech'
(not thought) bubble:
https://theentertainmentnut.files.wordpress.com/2014/02/lt102.jpg?w=479
So
yes, Snoopy is can 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 pilot fighter 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.
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I cannot recall any instance where a human character responded as though Snoopy's thought balloons were directly communicated to them.
Generally, his communication with humans was limited to his actions (not eating when fed; dancing about; kissing Lucy; Linus commenting on the "vulture" in a nearby tree; etc.)
As JohnP pointed out, Snoopy's thought balloons do seem to be communicated to Woodstock and his bird friends as though they were spoken, and to Snoopy's siblings when he meets up with them.
His siblings responses are communicated the same way; however, the birds' responses are always in "bird language" (||\|||/|||!).
It seems reasonable to assume that Snoopy (and his siblings) are communicating in "dog language", and the thought balloons are simply translations to simplify things for us.
We'd also need to suppose that birds understand "dog language"; however, since Snoopy seems to understand "bird language", that doesn't seem like much of a stretch.
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The closest we see to direct interaction is Woodstock and Snoopy.
Snoopy thinks in normal thought, while Woodstock speaks bird, yet they clearly understand each other While we don't see the other characters interact with the bubbles directly, there's always Snoopy's typewriter, which we do see some characters interact with directly from time to time
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No, they don't.
This is explicitly stated in the January 27th, 1997 comic strip.
However, Charles Schulz was not renown for his consistency, so it's possible that there exists another strip that contradicts this one.
scifi.stackexchange.com/users/89771/TheAsh
In Peanuts, are the humans aware of what Snoopy is thinking? I know that Charles Schulz was very careful to always place Snoopy's thoughts in a thought bubble as opposed to a speech bubble, but did the other characters react as if it was spoken?  I'm referring to human characters only here, not Woodstock or the cactus that Spike speaks to.
In Peanuts, do the human characters know what Snoopy's thinking?
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<comics><peanuts>
scifi.stackexchange.com/questions/180834
scifi.stackexchange.com/users/89771/TheAsh
There is no agreement as to whether the human characters were aware of Snoopy's thoughts. Some may feel that there is evidence of some understanding of his thoughts, but the comic strip in 1997 explicitly stated that the other characters were not aware of what Snoopy was thinking. This being said, Charles Schulz was not renowned for his consistency.  Charles Schultz himself stated that none of the human characters understood Snoopy's thoughts, but he was known to be inconsistent and there are signs that the Peanuts children have some understanding of Snoopy's thoughts.
There is evidence that the Peanuts children had some understanding of Snoopy's thoughts. No, they do not, as Charles Schultz himself stated.