There is a system defined extended stored procedure called xp_dirtree. You won't find any microsoft documentation on this - it is unsupported. It's easy, it's built in, but use it at your own risk. It could theoretically disappear when you upgrade your SQL install.
Alternatively, you can use xp_cmdshell, but the general advice to disable this extended procedure in sys.configurations, because it is inherently dangerous.
You could write your own CLR stored procedure. Jonathan Kehayias has an excellent article on this.
You could write your own application or service to manage your backups.
Or you could buy one of the several products which manage this kind of thing. A recommendation on which one is not really on topic for stackoverflow.