It is possibly true that at least some of the human characters in Charlotte's Web can be determined by their appearances. Fern's family: her brother, parents, and extended family who live nearby, behave and speak pretty much the way one would expect farmers of that era and place to behave.
The animal characters in Charlotte's Web, however, cannot necessarily be determined by their appearances.
One would not expect that a spider, a pig, and a rat would have much intelligence and emotion (at least intelligence and emotion as we humans perceive it) Yet, they do!
Charlotte's physical appearance as a spider, is so inconspicous, that humans would hardly notice her. Yet, she was capable of great things, especially for Wilbur, the pig.
Wilbur, the pig, while certainly big enough to be noticed by animals and humans alike, was helpless to change his situation. Until Charlotte took pity intervened for him, he was destined to become bacon and pork roasts by the time the first snowflake would fall in the coming winter.
Charlotte, by expertly spinning her webs, and supernaturally knowing how to spell the words used in her webs, defied her physical appearance.
To the humans in the story, it was nothing short of magic that Charlotte could spell out the words "Some Pig" in her webs as a description of Wilbur.
Another thing that shows that the characters cannot be defined by their physical appearances is that the animals in this story converse freely. Fern, although a human girl, witnesses and understands this, her family and community members do not.
Ultimately, Charlotte saves Wilbur from being slaughtered because she let the world know that he was extraordinary, and because of that Fern's family allowed Wilbur to live out a natural life and was not slaughtered for meat to sell and feed their family.