ACR TURBOPROP CREW OVERSHOT ASSIGNED ALT ON CLB IN ZAN AIRSPACE.

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WHILE CLBING THROUGH 12000 FT FOR 14000 FT; DISPATCH CALLED TO LET US KNOW THAT THE WX AT OUR DEST ARPT (SAND POINT) HAD DETERIORATED TO BELOW MINIMUMS. I ASKED THE CAPT (PF) IF HE WANTED TO CONSIDER A CHANGE OF OUR ALTERNATE ARPT AND WHILE HE RESPONDED; I NOTICED WE WERE CLBING THROUGH 15000 FT. I TOLD HIM AND HE DSNDED TO 14000 FT. OUR COMPANY'S OPERATIONAL PROC IS FOR THE PNF TO CALL OUT 'ONE TO GO' WHEN THE ACFT IS 1000 FT FROM THE ALT CLBING OR DSNDING TO. I HAD NOT MADE THAT CALLOUT. ALL 3 OF US COCKPIT CREW MEMBERS WERE SURPRISED BY THE RAPID DETERIORATION IN WX CONDITIONS (THE ARPT DOESN'T HAVE TAF'S) AND WERE SUBSEQUENTLY PREOCCUPIED WITH DISCUSSING THE POTENTIAL OF A MISSED APCH WITH A MINIMAL (BUT LEGAL) FUEL CONDITION. THE BREVITY OF THE PORT HEIDEN TO SAND POINT LEG (35 MINS) NECESSITATES A LOT OF COM AND COORD WITH ATC AND GND CREWS IN A SHORT PERIOD OF TIME; SO PROBS MUST BE DEALT WITH QUICKLY. HOWEVER; IN THIS CASE; AS IN ALL CASES; THE RULE IS TO FLY THE PLANE FIRST. I SHOULD HAVE WAITED UNTIL TOP OF CLB BEFORE DELVING INTO FLT PLANNING AND FUEL MGMNT ISSUES.