The good news is you're now close enough to your dates to get a good-ish sense of what the weather will be like. https://www.accuweather.com/en/pl/wrocaw/273125/daily-weather-forecast/273125?day=11
From this, it looks like the highs will be above freezing, and while there might be some snow the day before you leave, right now the 21st is predicted to be cloudy, but no snow.
How much gear will you have? I saw on your other post you'll need car seats, which is another issue to keep in mind, as far as costs. The Katowice airport, as mentioned, is pretty far from the city and its center. My memory was a taxi cost about 100PLN, and a quick look at the airport taxi website gave an estimate of 160PLN, or about $50. There's also a bus, which is cheaper, but you'll have to balance that with juggling your toddlers and luggage.
How tied into Prague are you? Are you visiting people there? Are you coming from Amsterdam? I only ask because, in playing around with the DB website, I noticed that one train goes through Dresden. And when I looked on Google Maps, it looks like Dresden in about an hour closer to Wroclaw (driving) than Prague. I think that route might be less mountainous as well.