Three-season tents, as the name suggests, are lightweight and built for use during spring, summer and fall. Though designed to withstand rain and wind in temperate climates, they're not capable of handling more than a few inches of snow. Additionally, these types of tents generally work best in established campgrounds where you don't have to carry your gear very far.
Sturdier four-season tents are specially designed for severe weather. Some of the features include an additional fourth pole meant to strengthen tent walls against heavy wind and snow, as well as a dome design that allows snow to slide off the top to prevent collapse and the concentration of cold elements. Keep in mind that because these tents are usually made of thicker material and have the extra pole, they're generally heavier to carry than three-season tents.
Other features to look for in selecting a tent for rough weather camping include a tub floor, factory-taped seams, and shock-corded poles. Instead of ending between the floor and wall of your tent, tub floors extend an inch or two on the side of the tent before connecting to the tent wall -- a design meant for waterproofing. Look for tub floors made of heavy gauge polyurethane-coated nylon taffeta or oxford nylon. Factory-taped seams have a waterproof material placed between overlapping seams, eliminating potential gaps once the tent is set up. Though this helps with water resistance, it's not technically a waterproof feature, so it may do better in less severe conditions. Shock-corded tent poles come in sections held together by an elastic cord that runs through all pole segments. These kinds of poles generally are easier to set up and collapse, especially if you're looking to move your tent around.