I have installed Windows 10 on MacBook Pro with Boot Camp. Now I would like to know if I should also install antivirus on Windows 10, or is all virus protection handled by the Mac?
Windows and Mac actually different OS run, so Mac can't handle all service on Windows.
Virus can run in Windows systems in virtual or native install. So you need install Antivirus on Windows systems.
Hopefully that's answer your questions.
Of course, installing an antivirus on your Windows is recommended, but it is not a necessity. Generally, if there was a virus, your mac would not be damaged, as the OS X file format is read only on Windows AFAIK (unless the virus was so well made, that it bypassed this).
or is all virus protection handled by the Mac?
There is no way for that to happen as when you run Windows with BootCamp, then Mac is not even running, and only mounted as a read-only format on Windows. It is almost like running 2 different systems.