Choose your battles wisely. Focus on correcting the behavior that is dangerous, there's enough of that type to worry about! No harm, no foul in wearing off season clothes in my opinion. Just be sure they're clean. Lighter long johns are made, try giving her a set of those for summer. My Dad was always freezing and wore 3 pairs of slacks and 3 or 4 shirts. Never broke a sweat even in August in Atlanta.
The clock, the calendar and the thermometer: In our house, all three are prominently displayed. There is no way anyone could miss the fact, especially if pointed out, that today is a beautiful sunny day in JUNE. Put her winter duds away and tell her that it's time for cottons and bright colors!
It may be difficult. My mom went through a stage where she cut up all her clothing. You can try removing all the long johns from her room and replacing winter clothing with summer options. Leave a few warm items, elderly have often have poor circulation and tend to get cold even in the warm summer months.
Put her winter duds away and tell her that it's time for cottons and bright colors!