A database snapshot cannot be backed up, either with SSMS or any third party software that I'm aware of. Technically since a db snapshot is viewed as a read-only database, a third party software could read the database and create it's own backup file... but it cannot use the SQL backup agents.

A Snapshot Backup is a not a database snapshot in the sense CREATE DATABASE ... AS SNAPSHOT, instead it's a method supported by SQL Server for performing database backups.

As BOL states the full, partial or file backup types can utilize this method for backing up a database. You are not performing a full/partial/file backup against a database snapshot created by the DDL statement.

David