"cold exterior" is correct and usable in written English.
You could use it to describe someone or something that appears uninviting or unfriendly from the outside. For example: "Although I know her, she always has a cold exterior when I see her in public."
Beneath my cold exterior, once you break the ice, you find cold water".
Her cold exterior was the result of an unsympathetic stepmother - her own mother had died soon after her birth.
Three-time Wimbledon champion Boris Becker "Behind [Federer's] poker face and cold exterior is an emotional young man as we saw with the scenes that followed his win.
They never say "Are you having a good time?" They play fiercely and they say only what they mean: "Despite this cold exterior our hearts are really full of soul".
Imogen should also pack her bags in anticipation however, as viewers are finding it hard to warm to her cold exterior and her inability to understand Big Brother's basic rules.
A thermal break is a piece of nonconductive material sandwiched between the front and the back of the door, preventing a cold exterior face from making the interior face cold, too.
Her character may be fiery on the inside, but her stone-cold exterior will hurt her in this tradition-bound contest.
His primary concern is his wife, Luz, who he tells us early on "has a cold, impeccable exterior inside which beats a soul as fragile and silken and easily crushed as a baby mouse.
It can be tempting to put on a cold, steely exterior but being yourself is the first step towards building relationships that will help you do your job better.
They have a cold, tough exterior that's hard to soften.
It was bitterly cold, and an exterior sensor, one of the many dotting their house, suggested that the nighttime temperature would dip far below zero.
