Well, you know there are mountains in SoCal so yes. In fact, there are mountains just 15 miles from downtown L.A. that get covered in snow at least a few times a year. But there’s also often frost in the inland valleys, and even sometimes near the coast, and even more in the deserts, as Johnny_L.A notes. Usually, around the end of December, there will be some nights where the temperature hits around 32 F. The idea of Southern California as this year-round tropical paradise was just something real estate boosters made up. In fact, last weekend we had chilly rain, so it was probably colder than places on the East Coast I saw on TV where everyone was celebrating in T-shirts.
I grew up in SoCal using the term Indian Summer, but it just meant some time in fall when things were especially hot–almost like an extension of summer.
To all the people planning to stop using this phrase, how about doing something more concrete to help Native Americans at the same time by donating to a charity? The Navajo have been particularly hard hit by Coronavirus due to isolation and lack of facilities, and 40% of families don’t have running water at home(!) making following hygiene rules impossible. There are charities offering both short and long term aid to choose from.
Another further suggestion (though not as helpful): generally avoid expressions built around a demographic identity. Using such expressions kindly and decently requires way more understanding and thought than most of us can bring to bear in the middle of a sentence that was about some other subject in the first place. Expressing something about a warm spell doesn’t need to trivialize an entire people.