It won't damage the tire but they will get harder as the temps go down. Even at 45 degrees they will loose 30% of their traction.

 

whew ok good. Not good about losing traction but that was somewhat expected. good to not damaging my new tires

 

Actually when I was shopping for tires I read a lot of the max summer performance tire write ups at TR and the only one I saw that had a low temp warning for storage was the Yoko Advan ad07 which said there was a damage risk below 14degF.

If I was daily driving where the temps were regularly or even sometimes below 40-45 I would strongly consider wheels and all seasons or even Blizzacks if there was much snow. IMO you'll probably end up taking some risks on summer tires you wouldn't ordinarily take under pressure to get to work etc. It's just not worth it.