Your withdrawal would then come from one of the colder wallets (not from the address you deposited to, and not necessarily the address your deposit was moved to).
I did that at first but with casinos. But you can do it only with casinos without KYC and without wagering requirements, which are almost non-existent nowadays.
To make potential outside observers lose track of my transactions on the blockchain, I deposited from different addresses of mine, but creating each time a different deposit address in the casino. Then I withdrew. The withdrawals always came from a large address that had nothing to do with any of the others, as my deposits had not yet moved from the original address. Once I checked a while after the withdrawal was done and I saw that my deposits had been consolidated at another address, which was not the one from which the withdrawal was sent to me.
If someone wanted to track me down, she was lost. Of course the casino will know more about me than an outside observer and the government might require the casino to give them information from me but good luck sending subpoenas to Curacao to find out what happened to a few hundred dollars in Bitcoin.
Obviously, mixers are better, but this type of "mix" can be used in some case, such as the one I have explained.