Your description is lovely and mostly correct. Here is a version with some slight grammar improvements to make the sentences flow better and be clearer:
"The woods are most beautiful in springtime, when everything is waking up from winter. Bird songs are getting louder as more birds come home. A cuckoo bird calls over and over, and a big owl makes deep 'hoot' sounds."
Explanation:
- Change "The wood" to "The woods" because we usually say woods when talking about a forest.
- "when everything is waking up from winter" is perfect!
- "Bird songs are getting louder with more birds coming home" is good, but "as more birds come home" sounds smoother.
- "a big owl is making deep 'hoot' sounds" is correct but "makes deep 'hoot' sounds" is simpler and clearer.
Overall, your sentence is wonderful and easy to understand for a 6-year-old.