I can give you general advice since i personally don’t live there.

First of all factor in where you will be living: you can use google’s street view or OSM Cycling maps to have an idea of the surrounding streets and of the city in general. The official transportation website of the city has very useful cycling maps.

In regard to it being cold, i recommend you search “Shifter cycling in cold” on youtube. Shifter is a channel dedicated to biking and they have gold advice on the matter. (Especially this video). Also, when you really dont want to bother with the cold, the public transport network is pretty fu**ing mentally massive and extensive (again KMK maps and it being eastern europe it is probably very affordable as well, so you might want to look at it. Outside of that, cycling in the cold is not an issue at all if you are prepared.

Safe riding and remember there are asshole motorists everywhere (not all of them are, but you just need one to ruin your ride).

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.

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.