If you are going for something realistic looking and/or you want to animate it. ( Move it around, rotate it whatever) I'd suggest looking into a 3d program. You could check out Blender ( free! ) Ive never used it but I hear its gaining popularity and some folks swear its as good or better than some retail 3d packages. Or you could check out Zaxwerks 3d invigorator plugin. Also, If youre not looking for something "photoreal" but still has some 3d depth you could try monkeying with cc sphere or cylinder and some deformed layers but I think it would be less of a headache to go for one of the many 3d programs out there.
As I'm sure you know, Invigorator isn't a modeling application, but you might be able to find a hat model for free or for cheap on turbosquid.com or elsewhere on the web. You'll probably need to find an .obj format model depending on what Invigorator is capable of importing.
Texturing the hat would be another issue that would likely be difficult in Invigorator, unless you just need basic colors and not a fully detailed fabric or something.
Your best bet, as Trevor mentioned, would be to go with a full featured 3D app. But most of them have a pretty steep learning curve, so it wouldn't hurt to search for a free hat model and give it a try with Invigorator first.