Welcome!
The snow tires typically have deep lugs and siping.
The lugs are for the snow that can be compressed into ridges, which provide bite for the lugs...so, for deep snow, deep lugs work best.
For wet roads/rocks and ice, siping (Little slits/holes in the tread blocks) helps grip. (Studded tires skid on wet roads more easily...)
Rubber compounds that stay soft and pliable when cold help a lot too...regular tire rubber can get too stiff to conform to the shape of the road irregularities, and lose traction, etc.
So - with that in mind, the only thing studs have a real advantage on is ice, and they suck on everything else....but on ice, they really help.
Snow tires are therefore not only good on hard pack (The harder the pack, the worse they will do, because the harder the pack, the more ice-like it becomes...), they are better in powder.
You might want a set of Bridgestone AT Revo's...great in snow and the wet, better handling than the stock tires too.
If you go off road a lot (Or plan to), the BFG AT ko's are great in snow too, but are more durable in rocky terrain (The Revos seem durable as well, but the BFG's are more durable).
Overall, the Revo's are better on road, and good off road....and the BFG's are good on road, and better off road.
If you want to go full on snow tire, the Blizzak's were tested as as good as a studded tire on ice...but they are a Winter tire only, if you leave them on, they could wear out before the next season.
You could click the Tirerack banner above this thread...the site has a huge database of tire reviews and rankings by category you could look at.
Hope that helps!
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- TJ
2001 Xterra '03 VG33, SE 5 spd, 305/70/16's, Revolvers, UBSkidderz, Doubled AAL's, 3"SL/2"BL, winch/bumpers, skids, sliders, OBA, Snorkel, pine stripes....
Friends don't let friends drive stock.
http://www.gifsoup.com/view/501230/tj-tackling-crawlers-ridge-o.gif