Tires are meant to drive on clear roads with plenty of good traction. They don't know what to do when it's ice and snow. But if there's good tread, of course it's better.
I was driving in some of this yesterday and I could feel the car doing some shimmying back and forth on it, slipping and catching itself, as there's patches of clear pavement mixed in with the slick.
A lot of thoughts go through my mind in these situations. Such as, Keep a clear focus. But then, Stop thinking about keeping a clear focus and just have one by nature. Too much thinking can distract your mind from what it's supposed to be doing.
There's a whole series of things your feet have to be doing. Letting up off the gas at particular times, pressing it at other times. Your eyes have to be looking far ahead and anticipating. It's a constant struggle.
The big thing that helped me get through the plodding pace (at times) was a recent viewing of the movie "Doctor Zhivago." I looked at the snowy fields and thought about Zhivago trudging across one, with icicles on his mustache. And the people traveling from Russia by walking hundreds of miles in the snow. At least I didn't have to do that! Suddenly 35 mph looked pretty good!