It is up to each of you to decide on what to do about how much you bring with you.
Two things to consider; 1) will it be more economical to buy some winter clothes using your country's Currency/money? 2) knowing though that you will have to pay extra money to bring a second suitcase.
Consider also that it is more difficult for one person to manage two suitcases when traveling.
@Mooyore; I would look online at a map of the airport in Dallas to see how far the location for international arriving flights are from the American Airlines terminal.