I'm starting riding lessons in the middle of winter in Minnesota....crazy, I know.
No, not crazy! I live next door in North Dakota and I don't ride indoors (usually) if I ride in the winter.
Never had a problem with my head getting cold under my helmet. I use an ear band designed to be worn under my helmet. I couldn't find a picture of what I have, but it just has a very thin band that goes over the top of my head so there is no bulk under the helmet - yet it keeps my ears warm.
And then I cover my helmet with a helmet cover like this one
I know that I will dress in layers, with warm socks, long underwear underneath my Wrangler jeans,--with perhaps some thin, low-profile snowpants on colder days--layers on top, etc.
Jeans? Oh no honey, not in the winter.
I wear a layer of under armor, followed by a layer of sweatpants, followed by snowpants (if needed). I have these riding snowpants
from horze.com and they are awesome!
I do wear my cowboy boots for safety reasons, but I will put some Toe warmers
on the TOP of my toes and that keeps my toes warm while riding. Then switch to my snowboots when I get off.