Not forgetting we don't see all the adventures so it's perfectly possible that other clothes are on the Tardis (their own) and we don't see them in it as they are being washed during the episode we are watching.
Lol, America's not getting a new episode next week - they have to wait 2 weeks before they get to see the second part of this story XD All 'cause of Memorial day. Not sure if they'll still show the finale on the same date, with a double episode, but I highly doubt it. Although they'd risk a LOT of people getting their Who fix from somewhere else if they delay the midseries finale by a week!
But it's cold outside and I don't want to be nekkid
It doesn't work like that. You would be taken up, but the clothes would be left behind, therefore it matters not what clothes you wear on this earthly plane.
On another note, I'm watching classic doctor who. It's interesting seeing the doctor not knowing who the Daleks are, and being completely helpless.
"The discovery of the Higgs boson led to limitless power, the elimination of poverty and Kit-Kats for everyone. It is a communist chocolate hellhole and I'm here to stop it ever happening."