You even can camp in the winter with a tarp. much depends on weather conditions like wind, snowfall and such. 4 season tents should be made to cope better with more wind and snowfall and generally need less pegs to errect (free standing, semi freestanding or a tunnel which can be eretcted with 3 pegs). But there are other methods to protect your 'lesser' sturdy tent against these elements.
1. secure all peg points and guylines. make sure you have pegs and/or bags suited to secure anchorpoints
2. During sleeping time wake every 2 hours (when two persons after every 4 hours sleep) to clear tent form snow and check pegs and guylines.
3. Take a snowshovel or something like it with you. You can dig a large hole to punt your tent in and with the dug out snow you can make a snowwall on the wind-side of the tent.
These tactics are even used with 4 season tents in extreme conditions.
But that doesn't mean a 3 season tent or a tarp cannot be used in winter. with the same precautions when the weather gets worse (wind and snow) you'll survive just as well.
remember when everything is pegged down and eventually still gets blown to pieces you'll still have pieces of the outerfly (you pegged is so it won't blow miles away just like that) to make emergency bivis form the fabric.
Good sleeping gear like a warm mat and sleeping bag and loads of common sence are more important than the quality of the tent IMHO. But a good tent makes life more comfortable. Thats the main difference, the rest is marginal when things get really bad.
One more thing 3-season tents tend to have loads of mesh in the inner. So it might get a bit more windy in a 3 sseason tent. a good windtight sleepingbag (a coated outershell) is enough to cope with that. it won't storm in your tent, the outer breaks most wind as long as it survives.