If she's not actually cold, go to Sam's Club or Costco and get a super soft luxious blanket she can cuddle up with. It sounds like she's keeping herself swaddled, so make sure the blanket is wrapped around her really good so she feels safe.
My mom does that also. She also likes to wear the hood. We bought her a very light summer jacket without a hood. We also put the other jacket out of sight so she won't see it and grab it. Sometimes we can convince her to go without but that's usually an exception not the rule.