Let's first examine a couple of differences that start with the basic original construction.
In looking at an end-on-view cross section, in a conventional plank-on-frame boat the boat exists as basically two hull-halfs that are held together by the floor timbers that span across the keel and connected to frames, of course there are variations, but in principle the planking, (garboard plank,) is fastened into a fairly shallow rabbet and much of the keel is external.
What keeps the boat together are those floor timbers.
In Cold Molding the preponderance of the keel is inside the boat. The keel is externally beveled/faired so that there is a large amount of faying surface for gluing/fastening, and then an external "wooden cap", if you will, is installed that covers up the ends of the veneers, spanning the width across the two sides.
As such the two halves of the boat are much more of a one-piece structure, floor timbers being mainly installed to serve as bearing devices for the interior structure and supporting engine beds and mast steps.
The key to success in cold molding over an existing carvel hull is making sure that the existing floors/frames are still capable of holding the halves together, as even with cutting a new rabbet for the veneers, that new rabbet will seldom have the large faying surface that transfers/supports loading to a full extent.
The same can be said of the stem.
As for the thickness of the new cold molded "covering", there are a lot of variables, thickness of individual veneers, fastening schedule, gluing properties of the wood, and the type/strength of the wood itself.
So far in this discussion we have had nothing to go on except "Can this be done".
How big is the boat?
How much does it weigh?
How thick is the original planking?
What type of wood is it planked with?
How are the planks fastened, nails, screws?
Power boat? Sailboat?
If power boat, is it a planing hull or displacement hull?
What type of design?
When these questions can be answered then some groundwork may be established for more specific replies.