As far as I can see, this would be very unlikely.
First, the virus would need to be distributed as a Linux binary - or anything cross-platform - and be smart enough to find a Windows partition. This is very easy to do (you can just search for a
Also, the virus would need to change the Windows registry, or other Windows configuration file, to enable itself. While the Windows API allows you to do those changes, a virus that ran on Linux would need to implement its own procedures to do them.
Finally, a spyware under your Linux web browser will not affect Windows. Probably the spyware would install under your
/home directory (since then it doesn't need to be root) which is not accessible from Windows (different filesystems).
All this would be more work (for the virus developer) for very little gain: at this point, it might be more profitable for him to target the Linux side.