Cold weather has a great effect on how our minds and our bodies work. Maybe that is why there are so many expressions that use the word "cold".
For example, people who show no human emotions or feelings are said to be cold-blooded. Cold can affect other parts of the body. But the expression "get cold feet" has nothing to do with cold or your feet. The expression means being afraid to do something you have decided to do. For example, you agree to be CEO of a company. But then you learn that all the other officers have resigned (辞职), and all the work of the company will be your responsibility. You are likely to get cold feet about being CEO when you understand the situation.
The expression "give someone the cold shoulder" probably comes from the physical act of turning your back toward someone, instead of speaking to him face to face. You may give the cold shoulder to a friend who has not kept a promise he made to you, or to someone who has lied about you to others.
"A cold fish" is not a fish. It is a person. But it is a person who is unemotional and shows no love or warmth. A cold fish does not offer much of himself to anyone. Someone who is a cold fish could be cold-hearted. He or she will never feel sorry for those in bad situation.
"Out in the cold" means not getting something that everybody else got. A person might say that everybody but him got a pay raise — he was left out in the cold. And it is not a pleasant place to be.