Blizzard was first shown at BlizzCon 2008 when the Wizard debuted, at that point a Tier IV skill in the Storm Skill Tree. It was a Tier V skill in the BlizzCon 2009 demo, which made it too high-level for players to select it.
Blizzard was again present in the BlizzCon 2010 demo, but still too high-level to play. Skill tiers were removed for the July 2011 Press Event, allowing skills to unlock steadily from levels 1 to 30. Consequently, all skill levels were adjusted and Blizzard became a level 26 skill.
The Diablo III Beta started in September 2011, and while it ran, all of the skills continued to undergo extensive iteration. Skill changes varied from changing the levels the skills are unlocked, to changes in resource cost, damage, and even function. A few skills were removed altogether, and a few new ones were added. Also, the entire skill system received an overhaul with the Beta Patch 13 update in February 2012, with physical runes replaced by rune effects that automatically unlock at various levels for the different skills.
Blizzard remained at level 26 when the beta started. With the Patch 13 changes, it was classified as an Arcane skill and moved to level 27. For March's Beta Patch 14, Blizzard was somewhat nerfed. Also, the category "Arcane" was renamed "Force".
Blizzard is a spell with a lot of heritage. The first version of this spell is seen in the classic WarCraft I from 1994 as a human Wizard spell (irony), and has been present in any Blizzard game (bar Diablo I) since. WarCraft II has it as a human mage spell, StarCraft doesn't have it, but has a very similar psionic storm, Diablo II has it as a Sorceress spell, WarCraft III has it as an Archmage hero ability and World of WarCraft has it as a Mage spell.
The principle is the same, with frozen shards dealing AoE damage, and is a staple spell in Blizzard Entertainment games that is unlikely to change any time soon.