Formation units all inherit escort's Movement speed.
Light cavalry proved excellent serving as escort to vulnerable bits of the army: commanders and headquarters, supply and medical units, artillery, communications and engineering troops, and such. Upon occasion, they were also assigned to provide security to civilians, notably to settlers and work parties; indeed, during the settling of the American west, South Africa, and Australia, light cavalry accompanied wagon trains, railroad work crews, freight caravans, and even stagecoaches (if somebody or something important was aboard) across territories full of hostile natives. The military escort, generally unhappy with such babysitting duty, tended to hurry these folk along at a brisk pace. Thus, making everyone happier when their destination was reached.