no pic attached.

Although I can't see the pic, I would say that Cupressus macrocarpa 'Goldcrest' is not particularly hardy I'm afraid, unless it is a well sheltered situation.

Once a branch has gone brown it is very unlikely to recover, sadly. They hate cold wind particularly.

You can remove the dead bits and tie some twine loosely round the bush/tree to keep it in shape until it grows again. I have done this and it works. (I was recommended to use old tights).