If you keep deleting more snapshots, you will eventually remove all of the snapshots that used those segments, and the segments will be removed and free up the disk space.
However, depending on your index & snapshot configuration you might need to remove very recent snapshots in order to achieve the reduction in disk space that you are after.
As an extreme example, if you have an index that is never written to, and you snapshot it every day, then each of those snapshots will refer to the same segement file.
If you delete a single snapshot, then it will recover a very small amount of disk space (cluster state, and metadata about the snapshot), but you would have to remove every single snapshot before the segment file was deleted.
Without knowing anything about your data, your merge policies, or you snapshot configuration we cannot tell you how many snapshots you would need to delete before the segment files would be removed.