We often fly between British winter and Australian summer. I never take a winter coat, but I do wear gloves and a scarf to the airport, and when we arrive at the departing UK airport I put them in my checked suitcase, along with the sweater I’m wearing. I fly in dressy trousers and a short sleeved top. Never jeans, as I don’t find them comfortable for long flights.
Coming back from Australia, when it’s upward of 100 degrees, I fly home in either shorts or a long, floaty summer skirt. I put my sweater and gloves at the top of my checked baggage and put them on before I leave the airport. I have also changed into long trousers at the arrival airport if it’s very cold, or I just suck it up and put on the heating in the car.
I would rather be a little cold in the airport than have to carry bulky clothes onto the flight.