INEXPERIENCED SINGLE PLT OF C150 ENCOUNTERS SNOW AND REDUCED VISIBILITY CONDITIONS WHILE OPERATING NEAR THE DC ADIZ AND INADVERTENTLY ENTERS THE TFR.

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BEFORE DEPARTING MANASSAS FOR HAGERSTOWN WITH MY INSTRUCTOR; WE OBTAINED A WX BRIEFING AND FILED AN ADIZ FLT PLAN FOR MY VFR RETURN TO MANASSAS. THE PLANE WAS JUST OUT OF AN EXTENDED ANNUAL AND THE PURPOSE OF THE FLT WAS TO RETURN THE PLANE TO MANASSAS. I DEPARTED HAGERSTOWN ABOUT XA05Z AND DID 2 STOP-AND-GO LNDGS TO CHK OUT ACFT. THE PLANE CHKED OUT FINE AND I STARTED ON MY FLT FROM HGR TO HEF. I HAD PLANNED TO FLY DIRECTLY TO MRB THEN TRACK OUTBOUND ON THE MRB 205 DEG RADIAL UNTIL I INTERSECTED CSN 355 DEG RADIAL; THEN TRACK THAT RADIAL TO CSN VOR AND THEN TURN E TO MANASSAS. I CALLED POTOMAC APCH FOR FLT FOLLOWING AND TO OBTAIN MY ADIZ SQUAWK SHORTLY AFTER DEPARTING THE HAGERSTOWN ARPT AND WAS TOLD THAT I WOULD HAVE TO CALL IN CLOSER TO MANASSAS. THE SNOW THAT HAD BEEN FORECAST TO ARRIVE SEVERAL HRS LATER; ARRIVED SUDDENLY AND MUCH EARLIER THAN FORECASTED AND VISIBILITY TO THE SW AND W BECAME OBSCURED BY SNOW. SINCE IT WAS CLR TO THE E AND S AND THE SNOW WAS COMING FROM THE W; I BELIEVED I COULD SAFELY CONTINUE VFR TO MANASSAS WITHOUT ENCOUNTERING SNOW AND WITHOUT IMPINGING ON THE ADIZ. INSTEAD OF TRACKING DIRECTLY TO THE MRB VOR; I STEERED A COURSE OF 190 DEGS; SLIGHTLY E OF MY PLANNED COURSE TO AVOID THE SNOW AND MAINTAIN VFR. I KNEW FROM MY PREFLT PLANNING; AND CONFIRMED WITH AN INFLT REVIEW OF THE TAC CHART; THAT AS LONG AS I STAYED TO THE W OF THE RIDGE LINE; I WOULD REMAIN CLR OF THE ADIZ. OVER HARPERS FERRY; WV; I CALLED IN AGAIN FOR FLT FOLLOWING AND MY ADIZ SQUAWK AND WAS TOLD THAT MY ALT WAS TOO LOW AND TO CALL IN LATER. BASED ON THE SNOW ENCROACHING FROM THE W AND MY INABILITY TO FOLLOW MY ORIGINAL FLT PLAN; I DECIDED TO FOLLOW THE SHENANDOAH RIVER SBOUND NOTING THAT IT WOULD KEEP ME CLR OF THE ADIZ. JUST S OF HARPER'S FERRY; I SUDDENLY ENCOUNTERED BOTH SNOW (WHICH REDUCED MY FORWARD VISIBILITY TO VFR MINIMUMS) AND MODERATE TURB (WHICH MADE IT IMPOSSIBLE TO BOTH FLY THE AIRPLANE AND KEEP TRACK OF MY POS ON THE CHART). THE WX HAD CLOSED IN BEHIND ME AND A RETURN TO HAGERSTOWN WAS NOT A POSSIBILITY. I WORKED TO FLY THE PLANE THROUGH THE WX WHILE MAINTAINING VFR. THE COMBINATION OF WX CONDITIONS REQUIRED MY FULL ATTN TO MAINTAIN CTL OF THE AIRPLANE AND KEEP THE AIRPLANE ON WHAT I BELIEVED WAS A 190 DEG HDG. AS SOON AS THE TURB SUBSIDED AND I WAS ABLE TO TURN MY ATTN TO THE RADIO; I CALLED IN AGAIN FOR FLT FOLLOWING AND TO OBTAIN MY ADIZ XPONDER CODE. I WAS INSTRUCTED TO IDENT; GIVEN A SQUAWK CODE; AND DIRECTED TO TURN TO A HDG OF 270 DEGS. I WAS THEN INFORMED THAT I NEEDED TO COPY A TELEPHONE NUMBER TO CALL POTOMAC APCH UPON LNDG AT MANASSAS BECAUSE I HAD INADVERTENTLY ENTERED THE ADIZ. WHILE ON A HDG OF 270 DEGS; THE CTLR PERIODICALLY ASKED ME IF I HAD GND CONTACT IN THE SNOW. I RESPONDED THAT I DID HAVE GND VISIBILITY; BUT NOT MUCH ROOM TO ASCEND AND EXTREMELY LIMITED FORWARD VISIBILITY. A SHORT TIME LATER; THE CTLR DIRECTED ME TO TURN S AGAIN AND GAVE ME VECTORS TO HEF. A FEW MINS AFTER TURNING S; I FLEW OUT OF THE AREA OF SNOW INTO GOOD VFR CONDITIONS. I FULLY REGRET THIS TFR INCURSION. I AM BOTH SORRY AND HIGHLY EMBARRASSED BY THE INCIDENT. I HAVE DISCUSSED THIS INCIDENT WITH MY INSTRUCTOR AND WE HAVE SPENT CONSIDERABLE TIME GOING OVER THE CIRCUMSTANCES OF THE FLT AND THE ALTERNATIVES THAT WERE AVAILABLE TO ME AT EACH POINT; INCLUDING DECLARING AN EMER. WHILE I UNDERSTAND EACH OF THEM; AND INDEED WAS AWARE OF EACH OF THEM; THE SELECTION OF ONE OF THE ALTERNATIVES REQUIRED RECOGNITION ON MY PART THAT I WAS IN TROUBLE. UNFORTUNATELY; I WAS NOT AWARE OF THAT DURING THE FLT SINCE I THOUGHT I KNEW WHERE I WAS. MY CONCLUSION IS THAT MY MISTAKE WAS NOT A DISREGARD FOR THE AIRSPACE RESTRS OR EVEN A NAV ERROR. MY MISTAKE WAS NOT REALIZING THAT I WAS STRESSED TO THE POINT WHERE I WAS UNABLE TO PERFORM ALL OF THE NECESSARY FUNCTIONS OF A PIC. WHILE I WAS ABLE TO KEEP THE AIRPLANE UNDER CTL; IN RETROSPECT; IT REQUIRED MORE EFFORT THAN I WAS AWARE OF AT THE TIME AND I WAS APPARENTLY UNABLE TO DEVOTE SUFFICIENT ATTN TO MAINTAINING MY POSITIONAL AWARENESS. I BELIEVE THIS INCIDENT HAS GIVEN ME THE PERSPECTIVE TO PERFORM A BETTER SELF ASSESSMENT OF MY CAPABILITIES AND I CAN STATE WITH ASSURANCE THAT I WILL NOT ALLOW MYSELF TO END UP IN A SIMILAR SIT.