
The term cool season perennial doesn't refer to the climate required for growing, but the temperature required for germination. These plants need cool temperatures and short day length to induce sprouting. They are usually planted in the fall in milder climates, and in the spring in colder climates. Alfalfa is quite hardy while maturing, withstanding high temperatures and drought. While it's not a grass (it is a legume,) this article can explain a bit more about cool season and warm season: https://www.gardeningknowhow.com/lawn-care/lgen/what-is-cool-grass.htm