Worthy of note: this rare clear shot of the full cowl from part 5 shows that it is super close to a part 4 cowl, as compared with a 3D print of the original part 4 cowl sculpt seen here.
It isn't entirely clear what happened to this cowl, which may be the same one worn throughout the film. It could be the one underneath the part 4 screen used mask, currently with a private collector. It could also be the one sitting in the Hollywood Museum with a mask used briefly in part 5. This cowl, though certainly an original part 4 pull and likely painted for screen use, has just some light bruising painted around the axe cut, rather than profuse blood flow, similar to the part 5 cowl. Suggestive, but hard to say.
Update: Crash posted a photo of a sculpt by Louis Lazzara that was evidently used for production of Friday the 13th Part 5. You can see that it is extremely close to the part 4 version, although the ears are somewhat differently shaped. So apparently its not the same, just a very similar sculpt. He may have had access to the part 4 to use as a model. Really interesting.