Directional textured dysprosium foils are fabricated by rapid solidification and sequential cold rolling, and the influences of their thickness values and magnetic structures on magnetic properties are analyzed and studied. The results show that magnetic properties of cold-rolled dysprosium foils are better than those of rapid solidification dysprosium foils, and the magnetization and permeability for each of the cold-rolled dysprosium foils are related to the thickness and temperature. Below Curie temperature, the cold-rolled dysprosium foils have obvious soft magnetic properties in a temperature range from 77 K to 4.2 K, the saturation magnetization for each of cold-rolled dysprosium foils increases by 5%－8%, and the saturation magnetization of 0.15-mm-thick cold-rolled dysprosium foil arrives at 2880 kA/m at 4.2 K, and the maximum permeability of cold-rolled 0.10-mm-thick dysprosium foil approaches to 30. The cryogenic magnetization of cold-rolled dysprosium foil with a strong external magnetic field is higher than that of conventional Co-V-Fe below 85 K. The cryogenic magnetic properties of textured dysprosium foils are related to the oxygen content and the orientation degree of (0001) crystal plane. The present study lays the foundation of technology and principle for preparing the chunky directional textured dysprosium soft magnet for cryogenic undulator.