Take a look at the solubility of paracetamol at different temperatures and the solubility of codeine phosphate over the same range. I've had to write a HR booklet on CWE for Lifeline Publications. The reference I used was:
Solubility of Paracetamol in Pure Solvents
J. Chem. Eng. Data, 1999, 44 (6), pp 1391–1395
Salt Solubility Products of Diprenorphine Hydrochloride, Codeine and Lidocaine Hydrochlorides and Phosphates – Novel Method of Data Analysis Not Dependent on Explicit Solubility Equations
ADMET & DMPK 1(4) (2013) 48-62
So, since you can actually see the data and even apply calculations, codeine will freeze with the water rather than crashing out. A slight ring of ice shows that the water needs to lose more energy to change phase (freeze) so it won't get colder until it has ALL frozen. You DO want it as cold as possible and you want to invest in a bottle of methionine capsules from the health food shop. While their are nifty A/B B/A back-extraction methods, for the average person, this data will keep you as safe as possible. In Manchester, people were resorting to smurfing pharmacies for Paramol when other opioids couldn't be obtained. We saw a dozen cases of severe liver damage.
No method will remove 100% of the paracetamol but if you are patient, take the amino-acid and don't make it a regular habit then it is safer than an unknown street drug (but far from perfect).