A winsome person is charming and pleasant, maybe even a bit lighthearted. We’re more likely to speak about a winsome woman, especially if the woman is capturing the heart of a man.
Winning often describes one aspect of a person: a winning manner, or a winning smile.
A team can be a winning one, but only if it is winning games. You would describe the U.S. women’s gymnastics team, which brought home 12 medals from the Olympic Games in Rio de Janeiro, as a winning team. You would also describe the five gymnasts — Simone Biles, Aly Raisman, Laurie Hernandez, Gabby Douglas, and Madison Kocian — as especially winsome.