Re: Is there any difference between these two expressions
And, of course, there is no indication in 1. that he was standing.
Also 1 describes a process, the second a state - unless you mean that, while frozen with fear, he stood up.
Re: Is there any difference between these two expressions
"Frozen with fear" has nothing to do with temperature. It refers to an inability to move - someone is so scared, they can't even move.
"Cold with fear" sounds rather strange to me. Although people shiver sometimes when they're scared, I don't think it's actually temperature-related.