If you already use iCloud and set up an account there, you will notice that all of your pictures in Photo Stream will be automatically stored on iCloud as your account has set up. If you want to delete the pictures
on iCloud due to any concerning problem, you always can do it.
As default, Apple will delete automatically delete pictures after 30 days or after 1000 pictures uploaded.
Instructions to delete pictures from iCloud and Photo Stream:
Step 1: Log into your iCloud.com account with Apple ID
Step 2: Click on the user name on the upper right corner
Step 3: Click on “Advanced”
Step 4: Click on “Reset Photo Stream”
Note: Click on Reset Photo Stream will remove all pictures on your Photo Stream and iCloud account but it will still be available on your device Camera Roll.