Wearing a beanie as a Tutor?

Not shit posting, I swear. But I reckon it might be a stupid question:

So I don't have time nor money to go to the barber and my hair is stupid + my home is quite cold. I'd love to wear a beanie during class to be self-confident and less cold but I worry about how my students might perceive me. Could it be perceived as a lack of professionalism? I've had students wear hats during my classes, but what about the other way around?

I know, stupid question, but appearance has its toll on online teaching so I'm just trying to make the right choice. Thanks for any input!

edit: thanks everyone!