You clearly understand the expression, though your choice of adjective in a stale scent is not particularly appropriate. I know exactly what you mean, but stale scents are often associated with such things as damp or smoky rooms or unwashed clothes or people, and can therefore be quite strong. The point about a cold trail is that there would be no scent.
Actually, as I understand cold trail, there wouldn't be a faint mark either - there would be no mark.
Still, this is unimportant unless you have to provide synonyms for some exercise or other. The main thing is that you understood the expression
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