First of all, a brief primer about tents - unless the tent has a stove in it, a tent will not keep you warm; you will be warmer in a tent that blocks the wind as opposed to one that doesn't (like one that is mostly mesh), but that's because a solid tent blocks the wind better. Tents with stoves in them like they use up North in -30F weather are a whole different story, so forget about them for the moment.
What keeps you warm is you, and no I am not being facetious. You are your own heat generator. A warm sleeping bag, warm clothes and plenty of food are what keep you warm. Anyone who tells you that a particular tent will keep you warmer than a different design other than the mesh/no mesh difference is wrong, with one slight exception-a small tent may be slightly warmer only because some of the heat you generate may slightly warm up the tent, but once you open the door, that's gone.
The big difference between a winter tent and others is how strong they are. My tent has five poles, four of which criss-cross above the tent floor, which is more or less a rectangle-the other is for the vestibule. I will post a picture of it, but the poles are hard to see. Look at a site like Hilleberg to see some serious winter tent designs. Mountain Hardwear, Marmot and North Face, among others, make winter tents.
My tent should withstand far higher winds than a summer tent, that's why it weighs twice as much as a summer tent of similar size (mine is a two person).
Where you are, I think a three season tent would work - it's not about temperatures, but wind and snow load, which for you will be moderate.
Cost - my tent cost me about $100. How is that possible? Simple, I bought it on eBay. There is a lot of cheap junk on eBay, but also a fair amount of really good stuff, like my tent, a discontinued model sold by EMS, a well-known East Coast brand. The trick is to figure out the difference between a good deal and junk. That takes time and research, but if you spend the time, it can be worth it. I also got a winter parka (the one on my avatar) the same way. Craigslist is also a good source, depending on where you are. I bought a nearly new winter bag off Craigslist for less than half retail. Not the latest model, but a quality down bag by a major brand with great customer service.
The bottom line is you probably don't need a real winter tent and if you look around and are patient, you can find great deals on used gear.
Note-in this picture, the front vestibule is folded back -it folds forward and it fairly large. The second photo is the interior of a TNF Mountain 25, another winter tent that belongs to a friend of mine, but you can see that this one also has crossed poles -also five if I remember right.