Being cold and being deathly cold are two different things.
I've only gotten mild frostbite once, but I'd never want to have it again. The skin blackens and peels, and itches like nothing I've ever experienced before.
Frostbite and hypothermia are two different things and often happen under different conditions. As noted, you can get hypothermia in (relatively) mild temperatures if you're wet, tired, dehydrated, etc. Frostbite tends to be the result of colder temperatures often in conjunction with wind. But, yes, both are bad. I've also had fairly mild frostbite of the ear lobes (a pretty common place) and it's not fun. The thing to be aware of though is that it doesn't have to be especially cold to get hypothermic. In cold weather hiking, some of the conditions you need to be most careful in are 35 degree or so rain.
I've only gotten mild frostbite once, but I'd never want to have it again. The skin blackens and peels, and itches like nothing I've ever experienced before.