But in the event that I use the 135's, should the winter tires I use have the same specs as the stock tires that come from factory on the car???
You can or you can change it a little. It's not usually done but you can put the front size on all four. Or keep them staggered and reduce the width in the back. Personally, I'd get another set of wheels...but I'm biased because I'd sell you a set.