Avalanche does not apply the slow effect on abilities that produce a mini-blizzard through the powers Iceburg, Cryclone, and Iceburg + Snowball Fight at any range outside of the mini-blizzard. Either this interaction does not work or the wording of mini-blizzard does not provide enough context.
I am assuming this is a bug since her power Blizznado does correctly interact with the mini-blizzard spawning powers.
Testing was only done in the practice range. Casting Blizzard the ultimate does create a noticeable slowing effect in the stated 20m range.