I went there 2 years ago. I lived in Alpensia resort and just ask the hotel to get me a taxi. I cannot remember the fare but it is not expensive.
However, it is difficult to get the fish if you just use their plastic bait. The fish are too smart ( I look down from the ice hold and there were lots of fishes but they did not eat my plastic bait).
I think it is very far away. This fishing place is quite near Alpensia resort, And it takes around 4-5 hours from Icheon airport to Alpensis resort.
Actually, not worth to go that far for ice fishing only cos not so much fun. its very cold and very hard to get the fish. Also the fishing place is very crowded.