When Arad and Gojo looked around the beach, they found no traces of a sewer system, which probably made more sense than finding one.
To keep the sewer water from freezing, multiple spells would need to be used, especially around the exit point where the water is to be dumped into the sea.
Gojo knew that firsthand because he had to deal with it in his kingdom, but here, he expected the civilization of the long-lost kingdom to be advanced enough to solve that problem.
It seems that he was wrong, and the people of the ruined city had decided that the best solution to a problem is to eliminate the problem before it even starts.
A classic tale, you won't ever worry about feeding a horse if you never owned one in the first place.
As their search around the beach showed nothing after long hours of work, Gojo and Arad became certain that the sewers' dumping point should be in the forest.
