Lol true, it does seem to have something like that...
Rotibox Bluetooth Beanie Hat Wireless Headphone for Outdoor Sports Xmas Gifts https://www.amazon.com/dp/B00SBBZITI/ref=cm_sw_r_cp_api_glc_fabc_jUD.FbGMTA3HG?_encoding=UTF8&psc=1
I recently bought the "Original Turtle Fur Fleece - The Hat, Heavyweight Fleece Watch Cap Beanie" and can confirm that it fits big heads. This is fleece and maybe it is a doubled up 100 wt fleece -- decently warm. I may have to consider the merino model too as this one was such a nice fit.
https://www.amazon.com/gp/product/B005TKQQ68/ref=ppx_od_dt_b_asin_title_s01?ie=UTF8&psc=1
This Turtle Fur fleece hat fits my big head (probably 7 3/4") and is a bit thicker than the typical hat.
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https://www.amazon.com/gp/product/B005TKQQ68/ref=ppx_od_dt_b_asin_title_s01?ie=UTF8&psc=1
I have something like this, but cheaper. Not exactly the most inconspicuous, but it's something. This one's more subtle.
I just bought this balaclava, and it fits under my helmet and is super warm. I used to use a cheap beanie from Forever 21 and a facemask.