I think my feet and hands feel cooler than my core, even at temperatures that aren't that cold. But, eventually, they warm up. Unless it's windy...
I am not embarrassed to wear toe covers or booties or even use the chemical warmers when I've seen others wearing shorts! I've learned to tolerate MUCH colder temperatures for riding in the past 2 years.
Oh, I found my cycling winter boots on line and on sale for an incredibly cheap price. Keep searching. I think it was almost 50% off.