I have a Windows wallet with lots of funds in it, and my Linux wallet is empty and I'd like to store some Bitcoin there. Is it safe to launch Bitcoin-QT through Wine (only one will be open at a time), send Bitcoin, close it and open the other?
If you want to access your bitcoin on your Linux environment as well, you just need to export the private keys in your Windows wallet and import them to your Linux wallet.
If you want to keep part of your bitcoin in your Windows wallet and part of your bitcoin in your Linux wallet (so that you won't lose all your bitcoin with a hack), you could simply send some bitcoin from your Windows wallet to an address in your Linux wallet.
This ^ ^ ^
Basically, private keys are passwords for your wallet, think of it that way,
and your wallet can be accessed anywhere as long as it is connected to the blockchain.
Linux already has its own bitcoin software though, dunno why you'd use the Windows software,
so yeah, that's basically how it works.
What makes it secure is what makes your machine secure.
Have fun!