Can we migrate oracle database 10gR2 to cross platform
To answer your question if you can migrate a linux database to a higher oracle release on a windows platform: Yes you can.

There are a few things to keep in mind...

Linux and windows use little endian, unix uses big endian -- basically it depends on the CPU not so much on the OS.

If you want to minimize downtime and restore the database on the windows server while the linux server is still productive, you have to apply the archivelogs from the linux database on the windows database until you do the switch. Basically this should work but there are some bugs I faced when doing this. So I would not recommend this option at least not with 10g or 11g (never tried it with 12c). Oracle officially supports DataGuard with windows and linux from 11gR2 but as I said there are some bugs. It failed in 3 of 5 attempts.

I personally don't like export-import migrations because you always have some trouble with invalid objects, characterset conversion, missing data, missing public synonyms etc.

--> I would recommend the the following action plan:


shutdown the linux database
startup mount the linux database
create an rman backup
restore the database on windows
open the database with alter database open resetlogs upgrade
run catupgrd.sql
do post-upgrade tasks