It is best to transplant oakleaf hydrangeas when they are dormant. The best timing depends on weather conditions. Generally, the best time is late fall or early spring just before growth begins. The soil should be warm enough for new root growth to begin right away. That doesn't mean that you can't transplant the shrub in mid-winter. If you do so, be sure to watch watering very closely and mulch over the root zone to prevent the soil from freezing too hard.