A snapshot is a sparse file. The size of the file appears to be the size of the database, but it hasn't reserved that much space on the disk. The size on disk is much, much smaller, the size only of the data inside.
See the section in Books Online "Understanding Sparse File Sizes in Database Snapshots"
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability