Im not sayin this is true but what if you body adapted to you leaving your windows open and a fan goin? The body would be used to getting cold all night and trying to keep itself warm, it began to start storing bodyfat easier so it'd cut down on that.
Possible or no
No, adaption to temperatures like that requires generations to go through that kind of thing, though all living organisms have certain defences when put through certain situations.
Chances are to warm itself up it would store fat, not burn it anyway.
As to drinking cold water, its kinda the same with ice cream or whatever.
Your body tries to keep an internal temperature of 37 degrees, so when you drink cold water the body burns any excess calories for direct heat.