SF340 Captain was dispatched to a non-towered airport with AWOS out of service and no trained weather observer available. The airport was VMC upon arrival and the reporter elected to land.

Narrative

I was in command of the flight to our destination. During my pre-flight duties; as I was reviewing the weather; I noticed that the current weather for our destination was missing but there was a TAF. The TAF report stated that at the time of our arrival the weather was forecast to be light winds from the northeast with visibility being greater than 6 miles and no significant cloud cover. I found it odd that there was no METAR for our destination but after reviewing the NOTAMS; I didn't see anything stating that the AWOS was out of service. I was contemplating calling Dispatch to see if they had any info on the status of the AWOS but was distracted by the gate agent who wanted to know if we could fit three additional passengers. Because of the distraction of coordinating with the ramp and the First Officer for Weight and Balance numbers; trying to get the aircraft out on time; and get an engine started to cool down the aircraft; I forgot to call Dispatch. Takeoff; cruise and descent were all normal. I was the pilot flying and the First Officer was pilot not flying. During our descent into our destination; when the First Officer was conducting the descent checklist; he tuned in to the AWOS. The AWOS reported that it was out of service. I told the First Officer to call the station personnel to see if they had a trained weather observer available. They did not so at that point I told the First Officer to call Center to see if they had any info. Center had no weather info but they did have weather for two nearby airports which were both about 20 miles away from our destination. At this point we were 40 miles out and we could see the airport. There was no cloud cover and a full moon. For some reason; I was sure that there was a provision in the FOM detailing how we could use the weather from another airport within 50 miles of our destination airport if needed for VFR. So I elected to continue the flight and we performed a normal visual approach. After the passengers were off the aircraft; I called Dispatch to see what was going to be done for the morning. I was worried that the AWOS would still be inoperative and if weather rolled in; we weren't going to be able to leave. After I got to my hotel room; the Dispatcher working my flight called me and after I explained to him that I landed without any weather info; I realized my mistake.This event occurred because of several mitigating factors. First of all; when I first noticed the METAR missing before we even boarded the passengers should have clued me in that something was wrong. Unfortunately; trying to get additional passengers on board; talking to the ramp and gate agent caused a distraction in which I forgot my initial plan of calling Dispatch to double check. If I had called Dispatch; they may have been able to resolve the situation before we even taxied for takeoff. Once we did find out that the AWOS wasn't working; I could have taken the time to actually try to verify with the FOM to see if there was a provision for landing at an airport with the AWOS inoperative. At the very least; I should have called Dispatch to see if we were going to have to divert to our alternate.