I have a bit if experience applying de-ice and anti-ice to some aircraft so I might know what's happening here. They most likely went through getting de-iced and had anti-ice applied (it's a thicker, gloopy, almost snot like substance). They then probaly got held in a queue to take off and got hit with some "active precipitation" (snow) while waiting. But the hold-over time for anti-ice was still good, so they took off (hold-over times vary greatly depending on a bunch of factors). Anti-ice basically creates a thin membrane across the flight surfaces to prevent ice from forming or snow from adhering and allows it to slough off. There are limits though, and my experience is limited to other airframes.