They do call them "winter" tires now, as opposed to "snow" tires like in the past. Snow tires were often made of traditional tread compounds, but molded with deep, blocky treads and big open sipes. Old style snow tires would be better in snow than traditional tires, but were pretty hopeless on ice. Their tread compounds were a bit better than that in normal tires, but still hardened and became glassy as temps got to freezing and below.
Modern "winter" tires are made of two different types of tread compounds. The first one is sometimes called a "traditional" tread compound, and is a lot like the older compounds but better materials allow this rubber to stay pliable to much colder temperatures, well below zero degrees F. These compounds, combined with the ability to manufacture treads with numerous, intricate sipes, allows these tires to have much better levels of grip than the older "snow" tires. Tires that use these types of compounds can also be distinguished by higher speed ratings, by their capability to be studded, or are called "performance" winter tires. Examples of this type of tire would be the General Altimax Arctic and Firestone Winterforce.
The other type of winter tire tread compounds are the studless snow and ice type, which have a very porous, fast wearing tread compound that grips ice and snow incredibly well, providing practically studded tire levels of grip on ice. These will also always be advertised as "studless" winter tires. These tend to be more expensive than the other brand of winter tires. Examples of this would be the Bridgestone Blizzak and Dunlop Graspic.
There's also the mountain snowflake symbol that tire manufacturers are allowed to emboss into the sidewall. It represents a tire that has 10% better grip in snow and ice conditions than some standard, which means that many all-season tires that have more aggressive tread compounds and larger tread voids can achieve this, even though their performance is far from that of a real winter tire.