Don't be a weight weenie when it's counterproductive. You're riding for exercise and fitness anyway--you could even look at a heavier wheel and tire as a plus.
I ride year-round, and I'm not at all concerned about weight (I weigh 240, and my 64cm steel Atlantis, with fenders in winter and a rack year-round, probably comes close to 30 pounds--I've never been tempted to put it on a scale). I don't think tire tread matters much on dry pavement or even in rain (the contact patch of the tires is too small to hydroplane), but it can in snow or slush. A slightly knobby tire is going to have more rubber on it than a smooth one, and that adds weight. I'd rather spin the rotating mass than skid and fall down, so I tolerate that. I keep my winter tires on wider (and thus heavier) rims, but I'm not sure that's really a help--I got them at a great price. But they ARE stronger, to deal with potholes and the occasional ice chunk in the gutter.
Sometimes weight is your friend. I almost never break anything, and when I'm picking my way over winter roads, I'm not concerned about speed anyway.