Actually, this should really be called shelters for extreme conditions with snow since there are many places where “winter” could be handled with a traditional “three season” tent.  When I think “winter shelters” I am thinking something that can survive 50+mph winds, and a foot of snow or more falling overnight.  Things that help make shelter survive in the winter:

• Strong materials.  Often times mountaineering shelters are made from fabric which is 1.5-2x the thickness and strength of similar shelters designed for three season use. Poles are typically thicker and larger diameter.
• Supported surface area. Ideally support of the shelters walls is evenly spread, across multiple points so that when the wind is blowing or snow is sticking the room, the pressure is distributed through out the shelter. The larger the area without support, the more likely that the shelter will bow in, and that the pressure will be concentrated on a small area which is more likely to fail. For domes you typically want three poles which cross each other.
• Steep walls so snow slides off rather than accumulating and weighting down the shelter.
• Aerodynamic shape so winds don’t knock you down
• Snow skirt which help keep the shelter stable in wind, and also provide continuous support rather than having the support points being the few places that stakes or snow anchors are attached to a shelter.

I don’t do a lot of winter / snow trips these days. When I was doing more winter trips I used a MLD Duomid for solo trips, and a GoLite pyramid as my multi-person winter shelter. If I was purchasing a hard-core shelter I would likely look at Hilleberg or Macpac tunnel tent or a large pyramid with a titanium wood stove. There was a good thread on BPL about shelters for winter/snow.

In the winter / snow I have used  a number of shelters over the years.  In reverse chronological order:

• MLD Duomid (cuben): 1-2 person pyramid design. Good solo shelter with reinforced pullouts.  Ideal for 1.  Usable but tight for 2.
• GoLite Hex: Very light for space, especially if you dig out snow. Nice flexibility. Light and cheap compared to most 4-season tents. You can dig out a platform which gives you a huge space. Staking can be a bit temperamental to get set up right. I have used it with a sleeping bag cover and just a ground cloth. In more severe conditions really wished it had snow skirt. Some similar tarps are designed to take a small wood stove like Titanium Goat and Kifaru.  In ancient past shared a large pyramid tarp that did have a snow skirt with a pile of other boys.
• Integral Designs Mk1 (now made by Rab): Loved it as a solo tent. Reasonable weight. Not cheap. Bombproof. More or less same tent is the Bibler i-tent and the BD Firstlight made using EPIC.
• Hilleberg Nallo2GT – This tent is not the lightest tent, but has a large vestibule which is handy in nasty weather. Very well made. Popular in Europe.
• Warmlite 2R – Shed snow well when pitched tight. Good in wind. Middle will sag if not pitched tightly. The 2R is not as tall as I would like if I was going to be spending a lot of time in the tent. The vestibule having a floor was annoying but manageable. They also make tents larger than the 2R. Get a third pole if using size 3.
• Sierra Designs Stretch Dome… I had the first version. Roomy for 2, usable with three. Mine stood the test of time but was stolen from my car. Not the lightest solution. I continue to be impressed with SD’s commitment to quality and innovation though I haven’t used a modern SD 4-season tent.
• North Face V24 – Hasn’t been sold for years. Was bombproof and heavy.
• Sierra Designs 3-Man Tent from the early 1970s… Double walled three person tent which used three strait poles in a tipi like design with a hex floor.  Great size for two in winter, worked for three. Half moon zipper in the floor formed a cookhole for using a stove inside.  Some of my fondest memories are nights I spent in this tent with my dad as storms raged outside.

I have also used some 3 season tents / tarptents in the winter which worked ok if there was no or small amounts of snow.  When the was enough snow to blow into the shelter through the netting I was unhappy. Anything not protected gets damp.  Not recommended. 

Whatever you are using a tarp or tent, you need to keep your shelter in place. Typically snow anchors are more effective than stakes for this task. See a nice Snow Anchor Analysis