Those are unusual tongs but I think you are on the right path suspecting they are ice tongs. I've used lots of log tongs, peaveys, cant hooks etc but nothing that resembles those on the right. The long handle is the length of a peavey handle but they have a spike point sticking straight out the low end near the chain. Yours are cut off like a cant hook tip so it can only be used for prying the load on the chain up. The only thing I can imagine it being used for is if you had a timber frame the height of the chain, the wood handle could be kept horizontal while the hook was set to grip a block of ice (or something) and then with the short tip of the handle placed on the timber frame one could pry upward on the long handle and lift the block 4 -5 inches or so. This would allow someone to slide a sleigh, sled or toboggan under the block and transport the block of ice. Then slide a new block to the loading area and repeat.
The tool itself is the configuration of a long handled cant hook but instead of a hook it has the chain and tongs attached. It still only gives you the ability to pry the load up 4 -6 inches though. I'm interested to hear what others may know about it.