Insulating old extension roof

I bought a house with an old extension a few years ago and its somehow colder in the extension than it is outside. When it's windy the doors will move and theres huge gusts of winds. When I bought it I got 50mm insulation for all the walls and sealed the doors and windows. The one thing I didn't do is the roof and I can feel the wind coming from it. During the snow the extension was fine, when the roof was covered. I spoke to a roofer and he said not to take it down if it's not leaking, just rip the inside out and insulate it. There is just rockwool and that ugly wood that seems to everyone though was great back in the 90s. I'm wondering what should I use? I'm thinking rockwool, rigid foam boards, plasterboard then skim it?