I read a tek once for doing that for AC&C. Most people know that a cold water extraction still leaves behind the caffeine in AC&C, and you're mostly counting on codeine's solubility in cold water and using the least amount of water possible to maximize the amount of codeine extracted while minimizing how much "space" is left over for the caffeine. The caffeine that gets through can still make you feel like shit though, and so I saw a tek where you take the post-CWE caffeine/codeine water and run it through a Brita-type filter, and the activated charcoal will remove the caffeine but leave the codeine.
I never actually tried this to see if it works, but a quick google search for "caffeine brita filter" shows a ton of threads here and elsewhere where people have mentioned that they do it. YMMV, can't hurt, but might affect your codeine yields.
Other than that though, there's no reason to do this versus just using a coffee filter. Just pre-wet the filter, and don't squeeze the shit left in the filter afterward unless you then let that water run through another filter.