Great sentence — it's correct!
Here is a simple explanation:
- "The Arctic fox" is the subject (who).
- "molts" is the verb (what it does). "Molts" means it sheds and regrows its fur.
- The dashes — like these — add the extra information "sheds and regrows its fur." That information explains what "molts" means.
- "so it looks white in winter and brown in summer" tells us the result of molting: the fox changes color.
If you want a shorter or simpler version, you can use one of these:
- The Arctic fox molts, so it looks white in winter and brown in summer.
- The Arctic fox sheds and regrows its fur. It looks white in winter and brown in summer.
One small note: "molts" is the usual spelling in American English. In British English you might see "moults." Both are correct.