On a rooted device it should be possible to forbid certain apps to contact internet connection
How is this possible in CyanogenMod 10.0?
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An app like Root Firewall (needs root) should work.
☆ Block Internet access for any apps:
Go to Settings > Applications
Open the application you want to restrict. Scroll down to the permissions section and strike off internet access by clicking on the permission.
Alternatively you could use an application like LBE privacy guard to restrict access.
With this method you can restrict any permission.
Sometimes apps start force-closing when you revoke permissions so be careful!