heat rises and cold falls, so the cold air will stay in the subway system. there is no real need for doors/etc at the entrances as long as you're going down.

the subways themselves put off a substantial amount of heat (from friction, motor loss, etc - all inefficiency eventually becomes heat) and for example in london they have problems with heat buildup in the tube system. so air-conditioning the platforms is generally desirable and probably necessary (especially in a more equatorial climate than england).