From the Super Mario Wiki
Flurries are snowman-like creatures that appear in the icy regions of World 4 of Subcon. They first appeared in Super Mario Bros. 2 as enemies and soldiers of the 8 bits. They are named after flurries, which are brief periods of snowfall. They are the first Snowman species in the Mario series.
Super Mario series
Super Mario Bros. 2
In Super Mario Bros. 2, Flurries are clumsy enemies that run along the ice chasing after Mario. In most cases, they are easy to avoid, since they have poor traction and can slip off of the platform they're on to their doom. They usually appear in groups in an attempt to corner Mario or any of his allies. They only appear in the World 4.
Interestingly, Flurries actually have perfect traction in the rare instances that they can be led onto non-ice surfaces, in particular at the bottom of the second tower in World 4-3.
BS Super Mario USA
In the direct sequel of Super Mario Bros. 2, BS Super Mario USA, Flurries make their return and play the same role as in the predecessor. They only appear in the third world of the game, which is also the icy land of Subcon itself.
Super Mario Advance 4: Super Mario Bros. 3
Flurries make an appearance in the remake of Super Mario Bros. 3 for GBA. They appear in the accessible level Promo: Coro Coro Castle scanned by the e-Reader. There are two of them, one of which can help Mario or Luigi pass through the spiky path via standing on their heads, and get the Brick Block and/or the Advance Coin. These Flurries still move as if all surfaces are slippery ice blocks to them.
The Super Mario Bros. Super Show!
Some Flurries occasionally appeared in The Super Mario Bros. Super Show!, where they spoke, despite not having visible mouths. Due to Wart not appearing on the show, they work for King Koopa here, and one (Flaky) even had a name. Staying true to the spirit of the games, Flurries appeared only in episodes that are set in snowy environments, such as the Land of Ice from "The Bird! The Bird!" and the North Pole from "Koopa Klaus."
Super Princess Peach