Bit of a dodgy reference there, E! I've certainly never heard that interpretation before. 'Parky', meaning 'cold', has been around since the late 19th century. I'm not sure about north of England dialect, but certainly the word 'park' in Scotland does not usually mean that pretty green area in a town centre but rather an open field. (It's often used in the names of football stadia, too.) Consequently, I've always assumed that it suggested the chill one might expect to experience if standing in an exposed field...ie parklike/parkish.