As much as you think you should save old chats for when you may need them later, you need to know that iMessages take up a lot of space on your device. Did you know your device saves every picture, document, video and file shared through iMessages?
From your app list, tap on messages and you will be able to see how much space your documents and data from iMessages is taking up. You can further review the large attachments and delete them manually.
You can also delete old messages by selecting every single thread individually.
If you do not want to delete all the old messages, moving them to iCloud would be a great option as it will free up space on your device and you will still be able to access your messages when you need them, and from all your devices.
Who knows, you might just end up clearing up a noticeable amount of space on your device.