You will need to create the login and grant it permissions in the database before you create the snapshot. The "content" of the snapshot never changes, so if the login does not have access to anything in the principal database then when you create the snapshot, that login will not have access and never will.

If you are using a SQL Server login, you will need to specify the SID when you create the login on the mirror server. It will need to be the same on both sql instances. IF you are using Windows Logins, then simply granting the user access to the both servers is enough - in this case, the SID is automatically supplied from active directory.

Next, grant the login access to the database (on the principal) with the permissions that it needs.

Mirroring will now copy the relevant security information from the principal database to the mirror.

Next, create the snapshot.

That should be enough for what you need