I think Jesus was born in spring because the sheperds were in the fileds and they would come out at spring time
That is a good observation. You could google Israel’s weather patterns to confirm that shepherding was likely a spring activity. There may also be non-Biblical sources about the census that Caesar did that caused Mary and Joseph to travel to Bethlehem.
All in all, a very interesting topic for a historian to research.
When was Jesus born? is a good question to ask. Sometimes you need to ask more than one question when do your research. These two come to mind:
Where might the shepherds be during the other seasons? Why do we celebrate his birth at the beginning of winter?
By keeping your research questions in mind as you read, you are less likely to overlook other possible answers to your main question.
I hope you enjoy investigating this topic.
Dr. Phillips (grandpa the librarian)