PLT received a WX briefing aprx 1 hr prior to flt during which '...a chance of light icing' was forecast. Aprx 30 mins after takeoff at 6000 ft MSL light rain was encountered. The PLT stated that a small amount of ice began to form on the strut and he requested a climb to 8000 ft MSL. N91625 was then cleared to climb above the cloud layer, however, heavy icing began to accumulate and the ACFT could not climb above 7300 ft MSL. A 300 to 400 fpm descent developed and the ACFT was cleared to Dalton, GA, via radar vectors. The PLT reported, 'Suddenly, at a height of approximately fifty feet above the runway, the aircraft seemed to veer as though left rudder had been applied, although the rudder pedal had not been moved.' The ACFT then heavily contacted the ground collapsing the nose gear. A witness stated aprx 3/4 inch of ice was present on the leading edge of the wings, 1/2 inch on the fuselage and aprx 1 inch on the belly. It was also determined the ACFT was loaded aprx 200 lbs over gross weight.