Do snapshots retain the IP address of the Droplet they were created from?

No, snapshots don’t retain the IP address of the Droplet they were created from.

We assign Droplet IP addresses automatically and they cannot be manually reassigned after creation, but you can assign a floating IP address to a Droplet and then reassign the floating IP address to other Droplet’s as needed. This allows you to maintain the same IP address in your infrastructure but gives you the flexibility to point it at different or redeployed Droplets.

You can recover your Droplet if you have taken a snapshot of the Droplet or signed up for automated backups.
Destroying a Droplet destroys the backups along with it. You’ll want to preserve your backups first.
You cannot currently download DigitalOcean backups or snapshots, but you can use third-party tools to save your data locally.