According to my own headcanon, Hogwarts is cold and draft is because it was originally coated with the same type of plaster as every other castle at that time period was coated with.
The plaster kept out drafts, protected the stone and mortar from the weather, hid imperfections (weaknesses) from enemies, and made the castles look nicer.
However, the plaster wasn't 100% waterproof, and needed to be regularly re-applied.
The lack of re-plastering is why abandoned muggle castles appear to be made of stone.
When the Statute of Secrecy was signed, Hogwart's plaster was removed, and muggle-repelling charms attached to the bare stone walls, magically amplifying the appearance of the bare stone, preventing any muggle from noticing anything other than the castle's stony-ness.
Why the inside doesn't have insulating / draft-blocking plaster... I'm not sure. Over-enthusiastic cleaning charms?