The private RV parks or campgrounds will usually not open until closer to Memorial Day because that is when the majority of tourists show up, it has nearly nothing to do with the weather.
By early April you may encounter snow, or even a snow storm, but they are really quite rare by that time of year, except up here in the northern Hills, which has a better chance, but the snow doesn't stick around long by that time of year here either. We have gotten some heavy snows into May, so it still pays to watch the weather and plan accordingly.
f you haven't been to South Dakota before, it would be worth while coming later in April and spend more time in the Black Hills, also don't forget about Wind Cave NP. You can see more animals there than the wildlife loop in Custer state park. I am not taking anything away from Custer SP, it is a national park caliber state park, I just prefer Wind Cave NP more because of the wildlife viewing and less crowded roads. There is much more to that park than the cave.
