It would be important to know how you come up with the idea – ice storage might make sense for very specific cases, but a normal single-family house with modern insulation most likely does not fall into that category.
If cooling is the main reason, then other alternatives are better: air conditioning in the first place, and to a lesser extent passive cooling via heat pump. For the latter, a deep borehole is slightly preferable, but a ring trench collector works almost just as well (especially for heating). A ring trench collector is usually exempt from approval and more cost-effective (especially if done as DIY, otherwise not necessarily), but it also has disadvantages – depending on the design, the property will be heavily excavated, including temporary storage of earth masses, with corresponding impact on the property area (which then has to be "repaired"). We have a ring trench collector.