How to maximize and preserve horseradish potency without vinegar?
Freshly grated horseradish is going to lose some of its potency within minutes, let alone a few hours.  Isothiocyanate, the hot chemical in horseradish, wasabi and mustard, aerosolizes extremely rapidly, which is why your eyes water just standing over it.  So you can't preserve all of its potency.

The best way to maximize potency while storing it for a day is to make sure it has as little contact with air as possible, and to refrigerate it.  Vacumm-packing will do this, as well as simply finding a very small container you can fill to the top with grated horseradish and then seal.  If you have access to argon or other neutral gas wine oxidation preventors, then it might be interesting to experiment with them.

If you were storing it for a longer period, I would recommend vacuum-packing and freezing, but not for just a day.