The ushanka (thanks, /u/numba1cyberwarrior!) is the warmest and way better than any beanie! If your bf finds that won't work for him, I'd recommend a Turtle Fur headband. Though if it gets cold enough he might re-think his hat-aversion.
I use this headband over Aftershokz Air. It takes a little finesse to get a comfy fit, but I imagine a similar headband would also work with other types of earbuds.
I have a fur headband similar to this that looks amazing (good for formal things) and it does not overwhelmingly shout "FUR!".
Also an ushanka (good for casual things). Both look fabulous! They are light, fluffy, with lots of movement. And very, very warm, good for negative weather!
I have that trademark TR "big head" so adjustable things like the headband are better lol.
Something like this... It's just an extra layer on your ears that you can wear underneath your cap.You will definitely notice if your ears are getting too cold, it almost starts to get painful. If it's super super cold that day you will want to have your face, especially your nose covered as well. But you mentioned you had a scarf so you should be alright there.