There's a lot of science behind getting traction in snow. All snow is not created equal. Trelleborg Friction Spikes are probably the best tire for riding in snow although Michelin and a few others make a tire with carbide-tipped studs that will work. Granted when the snow is soft and over a foot deep Friction Spikes do not perform as well as on hard pack snow. The only time I've seen a paddle tire perform well in powder was when the rider used carbide-tipped snowmobile studs on the paddles. Once the tire digs down to the frozen ground you need something that will bite down for traction. If there's very little snow over frozen ground automotive studs in a standard tire will outperform friction spikes.
While Trelleborgs and other carbide-tipped tires are very expensive there is a trade-off. These tires will last many seasons if properly taken care of. My front Trelleborg is 12 years old and shows almost no signs of wear. My rear is 5 years old and while the studs do have some wear it still performs very well. Also the old Swedish-made Trelleborgs are much better than the newer ones made in the Czech-Republic.