Back to your trees (and the squirrels in them), I'm guessing that your trees don't all have the same characteristics, and therefore I wouldn't see them as the same character reused in different stories. Of course, we authors tend to write what we know, and if we've gotten to know a character we've created, it's likely certain aspects of that character will crop up in later works, though hopefully there will be enough differences to make it an individual in its own rights.