Indian Summer is a part of weather folklore that always sparks debate. Some of the confusion is caused by being unaware of its long history.
Long before there was Indian Summer, Europeans looked forward to a break in cold weather they called Saint Luke's Little Summer. This period of warmer weather occurred around Saint Luke's feast day, October 18. Many countries in the "Old World" had similar "little summers".
When people journeyed to the "New World" they brought their folklore with them. The American version of "little summer" is named for the Native Americans.
Warm weather following the first frost or freeze is not Indian Summer. It must follow Squaw Winter which is a short period of time with winter conditions including cold temperatures and enough snow accumulation to track an animal.
Indian Summer may last a week with temperatures reaching the 70s & 80s. The other key is higher humidity which causes a haze. Early settlers also saw a haze because the Native Americans had been gathering around fires to stay warm during the cold snap.