Dig the horseradish root when you are ready to prepare it. That will make a difference in its potency.
Wear gloves if your skin is sensitive.
Do not put your head directly over the root as you work with it because...
The intact horseradish root has hardly any aroma. When cut or grated, however, enzymes from the now-broken plant cells break down sinigrin (a glucosinolate) to produce allyl isothiocyanate (mustard oil), which irritates the mucous membranes of the sinuses and eyes.
From wikipedia.org - Horseradish
A recipe for Prepared Horseradish