Why does iron oxide form hydrous iron oxide while chromium oxide does not?
TL;DR: Guignet's green is a green pigment with composition $\ce{Cr2O3.2H2O}$.
Long answer
Chromium oxide is largely used as a green pigment in various industrial and commercial purpose as it is the only green pigment which can withstand both acidic as well as alkaline environment. It is also used as permanent paints for cements, distempers and paints. It can also withstand high temperatures, hence used for coloring glasses, enamels and pottery glazes.
Guignet's green or $\ce{Cr2O3.2H2O}$ is the hydrous form of the oxide which is used for similar purpose as the anhydrous form. This pigment becomes anhydrous when heated at 200 °C, hence not suitable for glass and ceramic industries.
It is prepared by mixing 3 parts of boric acid and 1 parts of potassium dichromate which is heated in reverberatory furnace. It becomes a dull red mass initially but swells up releasing oxygen to give a nice green color. It is then boiled with water whereby chromium borate decomposes to hydrated chromium oxide and boric acid. The precipitate is dried and separated while the mixture is washed with mother liquor to evaporate the boric acid.
$$\ce{2K2Cr2O7 + 4H2B2O4 -&gt; 2Cr2B2O6 + 2K2B2O4 + 3O2 + 4H2O}$$
$$\ce{Cr2B2O6 + 3H2O -&gt; Cr2O3.2H2O + H2B2O4}$$
Reference

S. P. Das Gupta &amp; H. N. Bose (1948) A Note on Preparation of Chromic Oxide Green, Transactions of the Indian Ceramic Society, 7:2, 60-63, DOI: 10.1080/0371750X.1948.10877850