Why had Hortons Bay become deserted?

This is explained in the opening paragraph of the story. Hortons Bay was once a town which had thrived on its lumber industry, being centered around a mill on the town's lake. The mill once filled the area with the noise of its sawing. Eventually, however, the town ran out of logs, having presumably cut down all of the available trees. All the lumber that remained was taken away, and the machinery was stripped from the mill, taken away on schooners. This effectively meant that "everything that had made the mill a mill and Hortons Bay a town" was carried away along with the contents of the schooners. Because everyone had been employed due to the lumber industry, everything in the town swiftly closed, including the lodging houses, stores, offices, places to eat, and so forth. The result was that within ten years, the town was completely deserted, having no industry to sustain it.