Except for socks, I gave up on both wool and cotton about 30 years ago. Craft makes excellent base layers. Ordinary synthetic bike jersey over that. Sun sleeves if warm, arm warmers if chilly, wind vest or wind jacket over the top if cold or raining. That works down to about 45° and raining. If you're cold, pedal harder. Don't stand around outdoors if it's cold or raining.
__________________
Results matter