OK, the science behind it all.
If you get frostbite in your feet, you still survive.
If you get frostbite in your hands, you still survive.
If your torso gets much below 35 C, you are in some trouble but you can survive.
But if your head falls below 37 C (‘normal body temp’), you start to lose brain function, and your brain starts to fail.
Guess what your brain’s heating priorities are?
So yes, you can have frostbite on your extremities while your brain is still at 37 C – because your brain has shunted all available warm blood to itself. Your brain is extremely cold-sensitive and will cheerfully (I exaggerate only slightly) sacrifice your feet if necessary.
If your feet are ‘frozen’, it is no use putting down booties on them: there is little or no heat flow INTO your feet at that stage. You might of course be saying ‘but my head is still warm’, and you would probably be right. Your head is looking after itself.
The solution is to put some serious head covering on, to limit any heat loss from your head. Your head will get ‘too warm’, leading you to think you should bare your head. Don’t. At least, not until your brain has sent lots of nice warm blood down to your feet to warm them up. In serious cases of frostbite, the warming of your feet can even be a bit painful. That’s fine: it means your feet are recovering somewhat.
This is why I pour withering scorn on bags and quilts which do not have any hood. The lack of insulation around your head means you WILL have cold feet, overfill notwithstanding. If all you have is a hoodless bag or quilt, then get yourself a nice thick balaclava and WEAR it in bed. You can even get down-filled ‘balaclavas’ or hoods for really bad weather.
It follows then that just adding a balaclava may push your bag or quilt another 5 – 8 C lower in usefulness. My Katabatic down hood weighs 59 g and is probably overkill for anything in Australia. My synthetic hood (BPL Coccoon) is 56 g and more than adequate in Australia. Often we just use a fleece hood or ski cap. But normally we rely in a simple flap hood on our quilts.

This shows Sue with fleece ski cap and flap hood on UL summer-weight quilt in a single-skin tent. She took the fleece jacket off later. It was frosty outside.
Cheers