Indeed. Volcanic ash contains many soluble metal oxide glasses, which react in contact with water. Calcium and magnesium salts, in combination with carbon dioxide, water, and sodium and potassium salts, specifically.
The human body has the last three in fairly high abundance, and the lungs are very permeable to ionic exchanges, meaning that inhalation of reactive calcium and magnesium silicate salts, would quickly cause both an ion pump emergency in the respiratory system, it would also form a hydrated mineral chunk very quickly, which would plug up all the alveoli in the lungs. The fact that these salts form fine, needle like projections when rapidly expelled by hot gasses under high pressures, and that they are floating around in the air like little stiletto daggers, is only PART of their danger.
Personally though, I am a total shut-in, and always have my windows and doors closed. If there was a sudden rain of deadly white "Snow" raining down, and everyone going apeshit about it, I would stay inside, turn off all sources of air movement inside the house, and then put wet towels under all the doors and windowsills. I would then wait for it to stop "Snowing", even if that takes weeks. Knowing that the time could be protracted, immediately after putting the towels out, I would fill the bathtub, and anything else I could find, with tap water while it was still available.
Most likely though, given the short distances, and the immense energy such a caldera explosion would have, I would probably be killed by the overpressure wave long before any snow fell.
So, it's probably moot anyway.