We present the results from an analysis of deep Herschel Space Observatory observations of six nearby dwarf galaxies known to host galactic-scale winds. The superior far-infrared sensitivity and angular resolution of Herschel have allowed detection of cold circumgalactic dust features beyond the stellar components of the host galaxies traced by Spitzer 4.5 $mu$m images. Comparisons of these cold dust features with ancillary data reveal an imperfect spatial correlation with the ionized gas and warm dust wind components. We find that typically $sim$10-20% of the total dust mass in these galaxies resides outside of their stellar disks, but this fraction reaches $sim$60% in the case of NGC 1569. This galaxy also has the largest metallicity (O/H) deficit in our sample for its stellar mass. Overall, the small number of objects in our sample precludes drawing strong conclusions on the origin of the circumgalactic dust. We detect no statistically significant trends with star formation properties of the host galaxies, as might be expected if the dust were lifted above the disk by energy inputs from on-going star formation activity. Although a case for dust entrained in a galactic wind is seen in NGC 1569, in all cases, we cannot rule out the possibility that some of the circumgalactic dust might be associated instead with gas accreted or removed from the disk by recent galaxy interaction events, or that it is part of the outer gas-rich portion of the disk that lies below the sensitivity limit of the Spitzer 4.5 $mu$m data.