The localized loss of near-surface excess ice on Mars by sublimation (and perhaps melting) can produce thermokarstic collapse features such as expanded craters and scalloped depressions, which can be indicators of the preservation of shallow ice. We demonstrate this by identifying High Resolution Imaging Science Experiment images containing expanded craters south of Arcadia Planitia (25-40 degrees N) and observe a spatial correlation between regions with thermokarst and the lowest-latitude ice-exposing impact craters identified to date. In addition to widespread thermokarst north of 35 degrees N, we observe localized thermokarst features that we interpret as patchy ice as far south as 25 degrees N. Few ice-exposing craters have been identified in the southern hemisphere of Mars since they are easier to find in dusty, high-albedo regions, but the relationship among expanded craters, ice-exposing impacts, and the predicted ice table boundary in Arcadia Planitia allows us to extend this thermokarst survey into the southern midlatitudes (30-60 degrees S) to infer the presence of ice today. Our observations suggest that the southern hemisphere excess ice boundary lies at 45 degrees S regionally. At lower latitudes, some isolated terrains (e.g., crater fill and pole-facing slopes) also contain thermokarst, suggesting local ice preservation. We look for spatial relationships between our results and surface properties (e.g., slope and neutron spectrometer water ice concentration) and ice table models to understand the observed ice distribution. Our results show trends with thermal inertia and dust cover and are broadly consistent with ice deposition during a period with a higher relative humidity than today. Shallow, lower-latitude ice deposits are of interest for future exploration.