I have a coldweather helmet cover too, for my Bell Citi or Metro. But I found thing stiflingly hot because it cuts off air circulation. (I live in a mild climate. Icy roads are rare enough to occasion comment. The pedal pals still talk about how I slid back down a hill I stormed up-- three years ago.)
What I wear instead, under the helmet, for night rides and winter rides, is a thin skull cap made for runners. Last year I bought one to try, and only yesterday I told my wife that if they come into stock again at Lidl to buy me several. I say skull cap but the thing is deep enough to pull over your ears and keep them warm, without cutting off your aural awareness of traffic approaching from behind. Some kind of poly-something, with a bio-something treatment so it doesn't smell too soon. Probably pricey as branded "sports" gear, cheap at the German supermarket in my Irish village, but it only comes into stock for four days every year...
When it gets really cold, I have a knitted woollen cap with a hard visor, designed in Milan and bought there, as perky fashion for young girls. Same deal over the ears. Unfortunately white, so occasionally it needs washing and it takes a while drying. I wish I could get another one. Also worn under the helmet. It looks like retro fashion, something Mary Quant might have designed back in the days of the Beatles, when John Stephen of Carnaby St cut my suits in such loud checks that at the polo people tried to place bets with me.
I also have a padded leather jacket for dawn rides in midwinter frosts, and angora underwear to go with it. I shivering roadie said to me once, "What the fuck are you smiling about?" He thought though I was sending him up, but I was just telling the truth when I said, "My angora are tickling me."