Open/unsolved or cold case

Today, let us do some hypothesizing about when a murder case moves from open/unsolved to cold case.
It is now three years and sixty-two days since that horrible day when Stacey Burns was killed. Ample time has passed for a valid discussion of what constitutes a "cold case" to be held.
There are some police detectives who would argue that a case never goes cold; rather, it remains in the open/unsolved category. I truly don't know if this is true or not since the New Hampshire State Police do, in fact, have a cold case division and it apparently is active in this case as detectives from that division have interviewed at least one person in Wolfeboro of whom I am aware. There may or may not have been  others.
Speaking in generalities, suppose a detective from a cold case division of a police department interviews someone more than three years after a crime has been committed. Does that mean that case has turned cold? Does it mean that other detectives who are not in the cold case division have stopped working on the case?
Do more recent cases with more current leads receive all of the attention of the detectives handling active cases and a case like Stacey Burns' keeps moving further down the list?
A police officer explained to me once that a cold case means there is simply nothing more the police can do in the present climate of information. Hmmm . . .
Just as in the last blog where I wondered when the killer finally will say to himself/herself, "I got away with murder," I wonder again when the authorities will say in reference to Stacey Burns, "this case is cold" or,  perhaps more troublesome, have they already said it?
Just wondering . . .
Duker