I don't have the link on my laptop (which I'm on at the moment), but on my main computer I have a link to some long costume noses. You could make one, but honestly, buying one would be cheaper and easier, and would probably look better unless you're really good with latex. Search for "Pinocchio" noses.
Though I suppose it also depends on the style of Ice King that you're making. If you're making a more realistic-looking Ice King, I'd buy a latex one. If you're making a more cartoon-looking Ice King, I've seen people make decent ones out of cardboard, which doesn't look real but it does look cartoony. It all depends on what style you're trying to achieve.
Either way, this would probably be a better fit in the General Construction Help section.