Unlike the traditional mining system in Rune Factory games, Tides of Destiny features a new mining system. When Winter Island is raised, your monsters will grow ores for you. The main player will then go to the island and 'harvest' the ores using the hammer.
Unlocking Winter Island
Electra will leave a request on the bulletin board after Ymir gains the ability to swim through gentle currents. The request will be labeled "the legend of stone flowers." When you go to speak to Electra, she will speak of flowers that she's heard of, and that they only grow in cold weather. Aden says that he will search for the island, which will be marked on the map.
Using Ymir, go the location marked on the map (C-3) and raise the island. Upon entering it, you'll find that it's design is very similar to Spring Island, but it's covered in snow and ice. The island has many planting points as well. If you use spirits to revitalize part of the island, an in game tutorial will explain that Winter Island is rich in minerals, although you cannot grow anything on it.
Growing ores is similar to growing crops. Use spirit magic on a planting point to create a small mound of minerals. Over time, your monsters will grow the ores, until they are ready to harvest. More planting points become available the more developed the island is.