Yes, it's possible, and "over the Internet" doesn't make the slightest difference, at least not from the technical side. When trying to access an UNC path, Windows will try to connect to it over both SMB and WebDAV (by default), and as long as it can connect to either service, it'll work.
However, security is a concern. Historically, the Windows SMB server has been a victim of many exploits and security holes – so much that some ISPs even globally block the SMB ports. So if you choose SMB, you should use Samba, not Windows, as the server.
Also, SMB currently uses a weak authentication method (unless within an AD domain), so if you access the SMB server over public networks, it needs to be limited to Guest logins only.
Alternatively, you could set up WebDAV, using something like Apache httpd as the server. Recent Windows versions support accessing WebDAV over TLS (HTTPS).