Dr. Thorleif Etgen and his colleagues has searched for a possible correlation with physical activity and incident cognitive impairment who are older than 55 years old, and have reported their findings in Archives of Internal Medicine.
The results were not startling as you have guessed: a little can be enough for being happy, and of course not forgetting your happiness; ie. moderate (physical activity <3 times/wk), and high activity (physical activity 3 or more times/wk) is associated with a reduced incidence of cognitive impairment after 2 years in a large population-based cohort of elderly subjects.
Arch Intern Med. 2010;170(2):186-193.