Both are grammatically correct. Is the sentence “being?” meaning winter? The order of the sequence doesn’t change the meaning of the sequence, just the nuances, like timing and emphasis.

For example, if you are speaking in this sentence, and you wanted to create suspense, you might choose the order, The Season I like the best is winter. However if you want your audience to understand what you are talking about, simply say Winter is the season I like the best.