Perhaps the weather system picked up something from elsewhere and dropped it there?
There is such speculation; maybe a dust storm or storms that blew northeast into Grant County from the state's Bootheel and southeastern Arizona. But the dusty dry lake beds produce dusty or muddy rain and not white rain. White could be from deposits such as gypsum, but it would seem it would be very much more localized. With this widespread event, I suspect it may have come from south of the border. Following the wind direction back southwest and looking at satellite photos may help solve it.