Late spring through early autumn is the best window. June brings green prairie and wildflowers; July and August are hot, bright, and exposed; September is quieter and often excellent for hiking. In any warm month, start walks early, carry more water than you think you need, and keep well back from bison.
Winter is possible but much more self-reliant. Roads, services, and weather can all become limiting factors, and the park's appeal is harder to enjoy without long daylight and open trails.