Since the Metro environment on Windows 8 lacks most of the .NET framework class libraries or contains a substancially pared down version, is it possible to execute a \"ping\
No, unfortunately not. ICMP is not supported in WinRT: IcmpCreateFile
and related Win32 APIs are only available in the "desktop" API partition. ICMP can be implemented using raw sockets but since these are not supported in WinRT (and usually require elevation, anyway), this option is also not available to you.
As the developer of a Windows Store network scanning tool myself (http://lanscan.rcook.org/), I'd love to be able to do this.