If you want to keep your ears warm but you don't like to wear a hat, look for one of the many varieties of ear-warmer headbands that are available where sports accessories are sold. The caveat: if you want a headband to wear during a hard workout, make sure you get one that is made from moisture-wicking fabrics. Many clothing stores sell ear-warming headbands for fashion, not necessarily for sports, and these headbands are less likely to fit your head well and stay in place during a workout. Also, if they aren't made from moisture-wicking fabric, you may find that your ears and forehead are warm, but sweaty.
For the best fit, choose a headband that is slightly contoured to fit around the ears, rather than one that looks like a perfect circle. You'll be glad for the snug curves when the winter wind is blowing.