Why would you want to? You've bought it, presumably, and it's official DLC, so it's a serious question.

You saved your actual game before loading/starting HoS?

Well - you only have to start up the save, ignore that you ever downloaded and installed HoS.
You loose nothing but a bit of HDD space, but gain the option to actually go back to HoS if you will change your mind later on.

So yes: "why would you want to....?" :)
But yes, HoS has an entry "programs and functions", so it can be deinstalled.

I just want to know if it would break anything if you started a quest or something.

If you have HoS content in your saved game and then uninstall it, then yes it will break your game.