The pilot's failure to perform an adequate preflight (did not remove pitot tube protective covering prior to flight) which resulted in an inaccurate cockpit airspeed indication during takeoff roll and subsequent emergency landing. Factors were, the pilot's diverted attention while performing his preflight (loose animal on the ramp), the pilot's failure to abort the takeoff after noticing an airspeed anomaly during takeoff roll, and the low ceiling (100 feet overcast) the pilot encountered after lift off and while returning to land.