If you're thinking of hanging "not quite dry" clothing up in your closet, be absolutely SURE your closet is properly vented to remove the residual moisture. Otherwise all of your clothing could wind up smelling a bit musty. Maybe a bathroom ventilation fan for the purpose but you would need to remember to turn it on whenever you have dampish clothing in the closet.

Another thing you will have to do is make sure that anything you hang up that is still dampish, has PLENTY of room for air to circulate around it. I have a tendency to squash things together in my closet but when I hang damp things up in the laundry room, I always make sure they have plenty of air-circulation space around them. So for me to have a door directly between closet and laundry room would never work. You may be more disciplined about keeping all your clothing well-spaced than I am tho.

If you do decide to put an opening between the closet and laundry room, I'd probably go with a pocket door. Then you could go ahead and put a hanging rod across the opening allowing you to reach in to hang stuff from the laundry room side and you wouldn't really lose any useful closet space.

I think your walk-in closet is big enough that it's worth it to sacrifice the wall space for a doorway between the two rooms. You'd probably want it to be a pocket door or just a passageway without a door or you're either (a) going to lose more hanging space with the door swing into the closet or (b) going to have a VERY crowded laundry room.

For hanging damp clothing, maybe you should put a clothes rod above your washer/dryer to hang damp items before they are moved into the closet.

The pocket door is a good idea :)