I used to live in Paris where it felt warmish when the temperature was around 10C. Now that I live in Hong Kong, 10C feels freezing cold, as you pointed out.
Maybe it's related to humidity ? Or maybe it's because there is no indoor heating at all, as seanmcdirmid noted.
Dew point. When you sweat your skin will rapidly drop toward the dew point. Where I live it varies thru the year from below 0 to about 80, always below the air temp of course. When you don't sweat your skin approaches the sometimes much warmer air temp.
30 degrees air and 30 degrees dew point right after a snowfall is sweater and pants time. This morning the dew point is only 10 degrees so I have to wear a coat although I didn't need to zip it up. No wind helps.
A highly effective way to get killed doing winter sports is to build up a massive sweat and then completely stop moving before drying out... An air temp of 10 degrees is laughable and more or less comfortable if you're not sweating, but a dew point of 10 degrees if you're all sweaty will quite effectively give you hypothermia and kill you. Or the hypothermia will make you stupid, and then everyone will wonder why the heck a smart guy was walking along the cliff edge etc. Sweating in the cold is very dangerous. I usually don't wear a coat while I snowshoe hike (although I carry it in the backpack), wearing gloves and a hat and goggles but no coat always feels weird for the first time each season but you get used to it quickly.
expectations and clothes. In Russia i never wore shorts in 10C which i do in CA (even at 5C :) In Russia it would be jeans, good boots, t-shirt, sweater, good jacket. In CA - shorts, light sneakers, t-shirt, light jacket. Getting caught in SF at cable car stop summer evening without jacket - you get to freeze like it would be -25C with wind in St Petersburg :)
50f in San Fran can feel downright chilly.
50f in Chicago is shorts weather.