THE NON-INSTRUMENT RATED PLT RCVD A WX BRIEFING & FILED AN IFR FLT PLN. HE TKOF ON RWY 34 AT 1517 MST WITH LOW CEILING &RESTRICTED VIS DUE TO FOG & LGT SNOW. THE TWR CTLR SAW THE ACFT LIFT-OFF AT THE RWY'S END, THEN LOST SIGHT OF IT. SOON THEREAFTER, THE PLT SAID HE WAS UNABLE TO GAIN ALT & WAS RTRNG TO THE ARPT. HE WAS CLRD TO LND ON ANY RWY. DUE TO WX, TWR PSNL DIDN'T SEE THE ACFT UNTIL IT WAS ESE OF THE ARPT IN A RGT PATTERN, IT THEN DISAPPEARED FM THEIR VIEW AGAIN (IN WX) BFR CRASHING. THE PLT STATED THAT DRG TKOF, THE ENG BGN RUNNING ROUGH AT ABT 200' AGL & LOST PARTIAL PWR. HE SAID HECIRCLED BACK TO THE ARPT AT MIN SPEED, LOSING ABT 50' PER MIN, DODGING BLDGS & TREES. HE ATMTD TO LND ON RWY 34, BUT THEACFT NRLY STALLED. HE THEN ATMTD TO LND ON RWY 3, BUT THE ACFT HIT THE PERIMETER FENCE & SLID TO A STOP. NO PREIMPACT MECH PRBLM WAS FND. THE 1525 MST WX AT OGDEN WAS, IN PART: 700' OBSCURED, VIS 3/4 MI WITH FOG & LIGHT SNOW, TEMP 30, DEWPOINT 27. ACCORDING TO ICING PROBABILITY CHARTS, CARB ICING CONDS PREVAILED. ARPT ELEV WAS 4470'