I don't think this is possible. Looking at the documentation on database snapshots they inherit the security settings of the base database at the time the snapshot was created.
A database snapshot inherits the security constraints of its source database at the time of snapshot creation. Because snapshots are read-only, inherited permissions cannot be changed and permission changes made to the source will not be reflected in existing snapshots.
Database Snapshots (SQL Server)
https://msdn.microsoft.com/en-us/library/ms175158.aspx
Joie Andrew
"Since 1982"