It’s doable, not all places are connected via dedicated bike lanes, but you can check it on online maps. From my experience there’s rarely significant coat of snow, but there may be icy patches, So being extra careful and having lower yire pressure help in those conditions. It crucial to get a good feeling of your bike before attempting heavier conditions.

I live in Wrocław, not Kraków, so I can’t tell you anything about the city specifics.

About the winter - recently winters in Poland are mostly snow-less and the temperature usually doesn’t fall very low as well. There’s a lot of rain, water, puddles and mud though. I think cycling should be kinda possible for most of the winter but I wouldn’t expect it to be very pleasant. I, for one, use my bike as much possible in summer but definitely prefer public transportation during winter.