Are you bottling or kegging?
Honestly I never cold crash my hefe or dunkelweizens. I usually only let it ferment out then give it a couple days at ferm temps to clean up a little then rack into a keg. You can however go too early to bottle and have crap loads of yeast in the bottle. Wheat yeast is very powdery. It will look like tons of cloudiness but it will settle and then after a time it will just be the left over really powdery yeast that is there. You really need to sample and let the beer tell you when it is ready, most the time it is the same process for the hefes I make, but sometimes they suprise me and need more time or less time depending upon a lot of factors.
I however would not leave a hefe or dunkelweizen of normal gravity sitting in primary for 3 or 4 weeks. I'm drinking them at that point.
Kegged: Millenium Galaxy IPA, German Pilsner. Apricot Blonde Ale, ACE Witbier, ACE American Wheat.
Bottled: Smoked Red Rye, Old Tanglefoot Barleywine, Tripel, Dubbel, American Farmhouse Ale