The diamond dust is a weather effect that takes place in Iccirus City, in the overworld displaying small icicles floating through the air. In battle it does not serve any weather condition.
Source: Bulbapedia's weather page.
Diamond dust: Small ice crystals twinkle in the air. Found on certain special days in Snowpoint City, Mt. Silver and Icirrus City. Diamond dust, however, does not have the same effect as other snowy conditions in battle and instead has no effect in battle.
December 31st (New Year's Eve)
January 12th (Developer's Birthday)
February 29th (Leap Year)
March 4 (US Release of originals)
March 6 (European Release of originals)
March 15th (Ides of March)
April 9 (Originals revealed)
May 1st (May Day/International Workers' Day/Labour Day)