Can a Virus Enter via Ubuntu and affect Windows in dual boot?
Solution 1:
It's certainly possible to infect Windows through Ubuntu. It can happen if you have an infected file that gets transferred from one OS to the other; however, an infected file that lives only on the Linux partition will probably not have any affect on the Windows OS.
The easiest way to keep Windows clean is to use an antivirus application in Windows. It might be a bit overkill to also install an antivirus app in Ubuntu as well; however, if you want, you could use something like ClamAV to scan files before transferring them to Windows. There's more info on ClamAV in this question on SuperUser.
The good thing about ClamAV is that it's an on-demand scanner, so it doesn't consume any resources when you don't need it. That way, when you transfer files from Ubuntu to Windows, all you need to do is scan them before copying them over to the other OS.
Solution 2:
In theory, yes there is a risk. In the real world - almost no chance.
Keep in mind that malware needs to be executed before it can do any damage. If you have malware.exe, simply having it does nothing, the file needs to be executed. If it's opening a compromised picture file, or running an exe, the code inside the nasty file needs to be executed.
Even if you have WINE or some other emulation system on your machine, chances are pretty good it won't do any harm to your Windows partition, because most malware just simply isn't looking for another partiton.
Malware and other nasties are designed to target the widest array of users, to ensure maximum penetration for little effort. I'd be willing to bet that most malware in the wild will be unable to affect your Windows partition, unless it's specifically designed to do so.
Solution 3:
It's certainly possible, although far-fetched:
If the Linux malware has read-write access to the Windows partition, it can then modify any Windows file that it likes, and that way infect the other partition.
The malware needs to be designed as cross-system, but with the sophisticated multi-vector attacks that we're seeing today, everything is possible.
The only protection would be to ensure that Ubuntu doesn't have write access to the Windows partition.