How can I view my backed up text in iCloud

Recover Deleted Texts

If iCloud is set to ON for text messages and you deleted some text messages then they are gone from iCloud so cannot retrieved!  If this is the case then it is all over and no need to read further.

 If you do not use iCloud for text messages then you can restore your iPhone from a backup on your iCloud account (if you use iCloud to back up your iPhone). Once you restore then your texts will only be as current as when the back up was created. Here is ➔ How to restore your iPhone from an iCloud back up.

The other option is to restore your iPhone from a backup that you may have created on your computer. Once again, if you restore your iPhone from a computer back up then your texts will only be as current as the day and time the backup was created. 

If you have a backup created on your computer and If you choose to restore your iPhone from your iPhone from it then here is how to do it ➔ Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Axel F.

You cannot view the contents of an iCloud Backup; you can only use the backup to do a full restore of a device. See: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Also, if you are using Messages in the Cloud, the messages are deleted when deleted from a device. Also see the following from Use Messages in iCloud - Apple Support

You can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch, and Mac. For your privacy, Messages in iCloud is end-to-end encrypted,* which means you can't view or access Messages online via browser. 

@Axle Foley and @FoxFifth, I appreciate the information y'all shared regarding backing-up and restoring sms/text feeds on iCloud.

Would y'all happen to know of a different system, app or method to transfer (back-up and restore) sms/text feeds from an iPhone X to another iPhone X, that are set up with different Apple ID's? Both of the phones are mine and I just got the new iPhone X all set up so I'm trying to find a way to transfer just the sms/text feeds without having to set my new phone up from scratch, again.

Sorry, I don't know of a way to transfer them from one Apple ID to another.