Deleting iCloud messages
Can I delete messages saved on iCloud without losing them from my iPhone?
iPad mini, iOS 9
Messages are synced with iCloud and saved also , when you sign in with account credentials at www.icloud.com using a web browser the menage app is not viewed Set up Messages on iPhone - Apple Support
You can delete messages from the device , simultaneously they are removed from iCloud Delete messages and attachments on iPhone - Apple Support
Note : you mentioned Can I delete messages saved on iCloud without losing them from my iPhone?
No .