WHILE EN ROUTE FROM DEMING, NM, TO WACO, TX, THE PILOT ENCOUNTERED DETERIORATING WEATHER AND ELECTED TO DIVERT TO BROWNWOOD, TX, HIS ALTERNATE. PRIOR TO HIS DEPARTURE FROM DEMING, NEW MEXICO, HE HAD RECEIVED A COMPLETE WEATHER BRIEFING. THE BRIEFER INFORMED HIM THAT THE WEATHER ALONG HIS PROPOSED ROUTE OF FLIGHT WOULD BE DETERIORATING. THE PILOT WAS UNABLE TO LOCATE THE ALTERNATE AIRPORT DUE TO REDUCED VISIBILITY AND THE LIGHT CONDITIONS, SO HE DECIDED TO LAND IN A COW PASTURE. DURING THE LANDING ROLL, THE AIRPLANE STRUCK A BARBED WIRE FENCE AND NOSED OVER INTO A CREEK.