Quite correct. Also flying around at 250 KIAS or more does wonders for ram air temperature rise so even as jets fly through icing areas, much less of ice clings to airframe than it would at typical turboprop climbing speeds of 140-210 KIAS. Not to mention media hysteria that every time turboprop crashes brings stories like "Turboprops are flying coffins in ice!". I suppose that Joe Publics who still remember Colgan disaster mainly think it was ice related.
This incident is a wonderful example of experience vs. knowledge. Capt was 63, he was TRE, he had 12 000 hrs, 4000 on type, he was formerly employed by BaE. And yet he decided to take-off with snow merely swept away from the airframe and with no anti-icing fluid on the aeroplane, despite the snowfall. Of course it's best to be both knowledgeable and experienced, but even the members of 10000hrs+ club sometimes have to do something for the first time in their flying careers. Outcome tends to be better if they know what they're doing.