That bike is equipped with Avid Shorty 4's according to the description (contrary to the URL). Avid Shorty 4's are just regular cantilever brakes, which are standard on most cross bikes. A cantilever brake looks like this:
Mini V brakes are a type of V-brake with short pull so they can be used with road levers.
A mini-V brake looks like this:
Note that its essentially just a small V brake with road-style pads.
Disc brakes are nice in that their stopping power is more independent of the rim condition than rim brakes, but people have been riding in winter with rim brakes for decades, so its not essential (but its something you may like to have for messy riding). My answer in this question gives some pointers to disc brake need.
A general note is that the bike you've selected is quite nice, and in places where you actually have to plan for winter, winter does some quite nasty things to a bike ridden often in winter -- you may want to go for something cheaper or depending on conditions switch to a cheap MTB. So, if you describe where you are, this may help someone give a better answer.