On your way through Island Park, pull in at one of the rental shops on the highway, they can sell you the needed sticker.
Out of state people pay the same as in state people, $32.50 each. Sticker expires 10/31.
You are not required to show your title, past registration for non-resident. Resident stickers = yes.
(I am currently a vendor for these stickers, so I'll share what I know about the coming changes)
This year things are changing. Idaho Parks and Rec is being absorbed by Idaho DOT. All resident sticker sales (snow, ATV, OHV, boat) will be done in-house at DMV, online or through mail. You will be able to buy your stickers online and ride with a print out of your receipt until you get the actual stickers in the mail. Some vendors have 2013 OHV stickers now. BUT they will be pulled by DMV on 7/1/13 from what I have been told. The sticker you may have bought for 2013 is still valid, its just that the local vendor will not be able to sell them past 7/1.
They "say" that local vendors will still be able to sell the non-resident snow stickers next winter, but haven't gotten final confirmation on that.