Yes, SD is an open carry state. I have lived right next door in Wyoming for a long time and often OC in SD. You will have to check the state laws website to verify for yourself if your cc "permit" is recognized there. It is always best to look it up for yourself.
If you OC, keep in mind that there are a number of places where your gun will not be welcome. There are signs on some businesses, and you need to verify for yourself if there are other prohibited places. I can't think of any off hand. Except for the universal prohibition on "federal property," we don't have that problem in my corner of Wyoming.
You sure you want to go to South Dakota? <grin>