This is a widely held belief that is completely incorrect. In fact the opposite is true...Paulr said:The tread on winter tyres is also designed to throw snow out of the depth of the tread - summer tyres tend to hang on to compact snow in the treads so they get even worse, particularly when they snow gets iced in the treads as well.
Winter tyres are designed to hold onto snow, partly in deeper, wider grooves (which are better at displacing more water) but mostly within the small sipes across all the tread. Rubber on snow has very little grip but snow on snow grips pretty well. If you don't believe me try sticking a piece of rubber to snow and then try it with snow (it's how a snowball works).
Here is a picture to demonstrate the difference. The visible tread that is contacting the surface with a summer tyre is just rubber (having usually filled the grooves with snow) whereas the winter tyre has snow hanging off it all over.

All season tyres are not much better in snow/ice than summer but notably poorer the other 90% of the time so in our climate are kind of pointless. I take the gamble of not being able to drive in snow and stay on summer tyres because they work alright on 364 days of the year. One day I may actually bother having two sets of wheels with winter tyres on one, but until I have a car with a big surplus in power over grip it's not really needed.
Interesting piece on winter vs all season: http://www.bmwblog.com/2014/11/26/season-vs-snow-tire-bmw-winter-test/ Note the winter tyre holding a lot more snow than the all season, which is not really any better than a summer for tread pattern, just the compound being a bit softer.