There are plenty of meteorological logger solutions that can measure temperature and precipitation, as the sensors required are quite simple. The question of power is of course a difficult one to answer, as it depends on when during the year you want it sampling. If during the summer a good enough solar panel with battery solution should work fine, but for the winter you would likely need to visit to replace the battery. It would probably be a good idea to bring many batteries initially and then just visit and move the power cables around when needed.

Alternatives if you simply require the data is to use global met models with good accuracy to estimate the temperature and precipitation at your location.

You might try Campbell's integrated measurement system. In Inner Mongolia, China, our micrometeorological measurement system still works perfectly in winter at -20 ℃.

You could try dataloggers from elitech!