General aviation pilot with Flight Instructor reported a near miss with an aircraft that was landing opposite direction at a non-towered airport during a training flight. The reporter identified an unreliable AWOS as possibly contributing.

Narrative

On Day 0; I was conducting a training flight from WDR as PIC (pilot in command) accompanied by a CFI in the right seat. We departed WDR using Runway 23 at approximately XA:50 and after performing maneuvers a few miles from the airport we returned to do pattern work. The runway in use was 23 which has a standard left traffic pattern.We had performed two touch-and-go's on Runway 23; making radio calls on the CTAF of 123.0 MHz on each leg of the pattern. At XB:29 I was about to touch-down for the third time when the Instructor suddenly exclaimed that there was what appeared to be an aircraft about to land at the opposite end (i.e on Runway 05). I immediately executed a go-around and side-stepped to the right of Runway 23. As we were approximately halfway down the runway we observed that an aircraft had indeed landed on Runway 05.The instructor made a radio call on the CTAF asking if the aircraft which just landed on Runway 05 was on frequency - no response.After completing more touch and go's we landed full-stop. After shutting down and parking we located the other aircraft. I approached the pilot and asked if the aircraft had a functioning radio. The pilot indicated that it did not. He said it was a ferry flight and he had just stopped at WDR for fuel. I told him we had been about to land on Runway 23 when the instructor spotted his aircraft and we had to take evasive action. I pointed out we were flying the pattern and had received no radio calls about his landing and had not seen the aircraft on ADSB.The pilot stated he had earlier seen wind reports for WDR and elected to make a straight-in approach and landing on Runway 05. He stated that after performing his pre-landing checks he looked up and saw our aircraft doing a go-around. He indicated that he should have entered the pattern instead of doing straight-in and apologized; clearly realizing the dangerous situation which had arisen.I asked if he had a hand-held radio but he said he did not; although that would be a good thing to have on-board.Had I not been accompanied by an instructor there is a very high probability that this would have resulted in a collision on the runway. When on short final the focus of a pilots attention is on the touchdown zone and not the approach end of the opposite runway; so the presence of the NORDO aircraft would probably not have been realized until in ground effect along the runway.The AWOS wind direction and strength reporting at WDR has been noted as 'unreliable' in the message for a couple of years and the METAR does not include any wind data. This may have been misinterpreted by the other pilot as meaning calm and been a contributory factor to the incident.Reviewing Track Log data for my flight in Foreflight it indicates that the go-around was initiated at an altitude (as reported by iPad internal GPS) was 984ft and approx. 300ft from the threshold of Runway 23. On an actual landing the GPS reported altitude of 919 ft; using this correction we were approximately 65ft AGL when the go-around was initiated.