We don’t provide anything like cold storage. However, you could split your data into several indices and put them in separate free applications.
As an alternative, you could use the Browse method and download your data for later use, then proceed with removing the records on your application to switch to a Free plan, which includes 10 units (10,000 records and 10,000 search requests). You will need to reindex when you want to upload the records, in the future.