Instead of getting a blanket to cover the chair, try a tapestry or large piece of upholstery fabric! These options will both drape nicely around the chair, but not be too fuzzy or warm on the skin.
Another option is to get an all-together new chair! A thrift store or garage sale are great places to look. If the one you find isn’t exactly perfect, just upcycle it with some paint or reupholster it … or both! This DIY chair video is a great place to get inspired for some painting ideas!