You can track the money going from the cold storage wallet into an account that the mixer service owns. Say it's 10.000 coins.
The mixer then transfers 37, 185, 205, 1002, and other random amounts to other accounts, which in turn transfers it to other accounts, and at some point they get funneled to one or more accounts owned by the person who originally transferred the money into the mixer.
Couple this with a lot of other people doing the same at the same time for the same mixer service, and you cannot say who owns the coins being transferred between the accounts. It is public what money was transferred back and forth, but without some serious analysis it's practically impossible to track who is likely to own the accounts where the money end up.
The mixer then transfers 37, 185, 205, 1002, and other random amounts to other accounts, which in turn transfers it to other accounts, and at some point they get funneled to one or more accounts owned by the person who originally transferred the money into the mixer.
Couple this with a lot of other people doing the same at the same time for the same mixer service, and you cannot say who owns the coins being transferred between the accounts. It is public what money was transferred back and forth, but without some serious analysis it's practically impossible to track who is likely to own the accounts where the money end up.