There are a lot of hurdles to get across in order to be able to do that.
First off is video. Galileo is not RassberryPi. It does not have video on the board, and getting video to work has been difficult for those who have tried.
Secondly, Galileo is a Linux computer. The BIOS is specific to bringing up the Galileo version of Linux (built using Yocto). People have been working on getting a standard Linux image like debian (https://communities.intel.com/message/225273#225273) to work with Galileo, but so far, that has not been successful.
Third, Windows is not compiled for the Quark processor. Unlike Linux, you cannot recompile Windows. So, if you did get it onto the Galileo, it probably would not run very well.
I won't go so far as to say it is impossible to boot window on a Galileo board, but it will be very difficult for the first person who tries it.
A RasberryPi is better suited for your particular use case. I think you can even download pre-built images that will do exactly what you want to do.
Personally, I like Intel's NUCs (Intel® NUC) for HTPCs, but they are a little more expensive.