Hobbs Heirloom washable wool batting would be my choice. It is warmer than cotton battings and comparable in weight to polyester (much lighter than cotton of similar warmth). Here is a link:
http://www.hobbsbatting.com/products/heirloom/
Hobbs also has a Tuscany wool batting, but I saw some negative comments about it on a longarming group. It might have been a bad batch. Someone here on the QB had a bad bearding experience with Quilter's Dream wool batting, so I stick to Hobbs Heirloom.
Wool batting is more expensive, but Connecting Threads is having a sale on batting right now and that makes it more affordable.
Edit: This website lists the pro's and con's of different batting types. Wool is the warmest, followed by polyester, then cotton. Wool and polyester are among the lightest in weight; however, wool and cotton breathe better.
https://www.createforless.com/buying...right-one.aspx