Tcoat: no, there are tires that are good winter tires and performance ones. Not road legal though

. - So called "saws" in slang, long-studded sport tires. With such on some tracks opened all year round on ice often track lap records are better in winter then in summer on dry tarmac. Of course, such studs are not fit due grip & damage to pavement for normal plown tarmac roads .. but still, you get both performance & winter in one package