Current 3D stylization methods often assume static scenes, which violates the dynamic nature of our real world. To address this limitation, we present S-DyRF, a reference-based spatio-temporal stylization method for dynamic neural radiance fields. However, stylizing dynamic 3D scenes is inherently challenging due to the limited availability of stylized reference images along the temporal axis. Our key insight lies in introducing additional temporal cues besides the provided reference. To this end, we generate temporal pseudo-references from the given stylized reference. These pseudo-references facilitate the propagation of style information from the reference to the entire dynamic 3D scene. For coarse style transfer, we enforce novel views and times to mimic the style details present in pseudo-references at the feature level. To preserve high-frequency details, we create a collection of stylized temporal pseudo-rays from temporal pseudo-references. These pseudo-rays serve as detailed and explicit stylization guidance for achieving fine style transfer. Experiments on both synthetic and real-world datasets demonstrate that our method yields plausible stylized results of space-time view synthesis on dynamic 3D scenes.