Transfer Oracle 10g Database From Linux to Windows
Restore should not be an issue. Both Linux and Windows are little endian so you are OK there. Are you using rman? You can always recreate the database on Windows and perform an export/import to the new database.
Ideally you want to just restore using RMAN directly to the Windows server.
Check out Chapter 4 of Oracle® Database Backup and Recovery Advanced User's Guide or even go with a duplicate or standby database depending on your needs, downtime time frame and licensing.
Please provide more information about your situation with respect to your backup type and tools.