After grinding, the chemicals in the root start a reaction. Heat starts to build almost immediately. At first it is difficult to know how much heat you like and want. Flooding with vinegar stops this process. I have never heard of anyone putting the vinegar in at the same time they grind, unless they want fairly mild horseradish. It seems to me that the grinding, the chemical reaction and the vinegar would work to counter balance each other. It would kill the action immediately. So I grind and time my delay in adding Vinegar. This lets the heat build, but in a somewhat controllable fashion. I usually split my ground root into three parts. I add Vinegar to each portion, after two, four and six minutes, respectively. I end up with mild, medium and hot horseradish.
I know everyone has different ideas and does things different, but this is how I do it, and have for years.
Good luck.. I know you will enjoy the results no matter how you choose to process it.