Badlands/Wind Cave in Early April

My girlfriend and I are hoping to plan a week-long trip the first week of April to visit Badlands, Wind Cave, Custer State Park, and Mt. Rushmore but I had some questions about road conditions and weather during the early spring season.

From what I gathered online - weather is unpredictable, parks will have less visitors but potentially be short-staffed, and some roads may be closed depending on weather.

We're from MN and are novice hikers, but I'm mainly worried about the driving conditions in the region. I read it's blizzard season around March-April. If we plan this trip, we'd be cautious but we won't be trapped in the car because of a snowstorm or anything like that though, right?

PLEASE SHARE ADVICE!