Because of the way heat travels, a floor loses nothing by convection, and very little by conduction.
The cold you feel will be draughts, these are pretty sure to be coming up the gap under the skirting boards, from the ventilated void beneath. Black stains are from dirt and dust blowing up.
The best way to cure it is to take up the floorboards against the external walls, and pack the first foot with mineral wool (taking care not to block air bricks) between the joists and against the wall. Clean out all the dirt first with a small brush and a builders canister vac (building dust is gritty and damaging to domestic vacs).
The easiest (but not the best) is to pack the gaps under the skirting with foam or cork strips (don't use expanding foam, you will never clean it off)
As you have carpets, not bare boards, you will not be getting significant draughts through the rest of the floor.
If you ever need to take up or renew a floor, you can pack the whole thing with mineral wool berween the joists for a first class job. You staple mesh to the joists first to prevent it falling through the gaps.
The first foot, against the external walls, is the most important.
Modern mineral wool, treated with ecose, does not shed irritant dust or fibres. It is brown. I will never use yellow fibreglass.