Is it okay to leave blankets on a basement floor if it's right next to your bed?

I have two blankets I really like and use frequently, but I don't like having on my bed (due to them being too warm). If I had them on the floor overnight when I don't need them, would it damage the blankets?

Basement is always chilly (below 70F), even during summer, so I have good reason to believe it is climate controlled.