Step 1: "Either" is used in negative sentences to agree with a negative statement. In this case, the speaker is agreeing with the idea that they don't need the woolen sweaters.
Step 2: "Anyway" is used to dismiss the importance of something but does not fit the context of agreeing with a negative statement.
Step 3: "Neither" is typically used in a context where two negative choices are being discussed, and "too" is used to mean "also," which doesn't apply here.
Thus, the correct answer is "either."