I really had fun with this one. You know what would make it even cosier? Being able to choose a small avatar for ourselves. The mouse pointer as your icon feels a very impersonal at the moment. Having avatars would make it feel more like we're all hanging out together in this wonderland.
It's not what you asked for, but right click to choose an enhanced icon. (EDIT: Oops that appears to just be a temporary emoticon)
You can put the hat on. It's in the main camp building in a bedroom. Your cursor will be wearing a hat from then on.
You can also put other clothes on, like sunglasses and shorts.
Can you don multiple items? Didn't try.
Yeah you can. You buy them with seashells.