I do horseradish every year and yes I use a food processor. I like that little 4cup model from Cusinart. Cut it into chunks, add to the food processor and process, do not make mush; and be careful when you take the top off. Stand back or you can burn your nostrils, eyes etc.
Actually, it's vinegar that stops the heat process. 2-3 TBLS of vinegar, for each cup of horseradish. Later, you can make horseradish cream, etc. I have had it last a year, in the IKEA glass canning jars, in the refrigerator. Use your own judgement, if it looks off.
