My cold weather tires are Vittoria Randonneur Cross. Not too heavy, great traction, great flat protection and decent rolling resistance. I use the 26" version, but they also come in 700c in a variety of widths. When the weather gets bad, I swap out with studded tires on the 26" wheels. My warm weather 26" tires are Conti Sport Contacts (slicks).

I use Gatorskins/4 Seasons year round on the 700c wheels. Never had any issues as you describe.