WOODY the brand new summer tyre will never outperform even a half used winter tyre in cold or snow, the compound used and the thread pattern with a lot of small cuts which open when the tire meets the surface and close as it goes off just bites into the snow, they are also a lot better in the cold with no snow, summer tyre needs a higher temperature to provide the grip you need, the winter tire pretty much works well from cold, so even when there's no snow the winter tire will give you better performance, an example, check the monte carlo rally tyres, even when there's no snow they never use typical soft slick's nor intermediates, they use the winter compound with winter thread, back in 2004 I was running a Polish rallying 2nd league, a rally run in march, 70 km of special stages, temperature around zero C, there was no snow on the road, the tarmac was cold though, I was running bridgestone potenza's RE720 175/50/13 in my seicento gr. N, the class winner was running fulda winter tyres 155/65/13 and they were unstoppable, the reason to this, a summer tire will never warm up to its operating temperature to provide the grip it is designed to provide, so yes, all our classmates running on summer tyres got beaten by a few smart people with the winter tires on.
I recommend getting the snow tires, you will be able to have some fun in the snow as well! the 197 is really nice in the snow! but you need the tires!