Fuji, the highest mountain in Japan, is 3,776 meters high, so no matter how close it is to the sun, it is only about 4 km closer. The distance between the earth and the sun is about 150 million kilometers, so even if we were only 4 kilometers closer to the sun, which is that far away, it would not be considered very close. In other words, the fact that it is cold on top of a mountain has nothing to do with how far or close it is from the sun.
What is responsible for the coldness is the air. The earth is surrounded by air. The air around the earth is called the atmosphere, and the higher up in the atmosphere, the less air there is and the thinner it becomes. The higher up in the atmosphere, the less air there is, and the lower the pressure becomes.
The lower the pressure, the lower the temperature, so the higher the atmosphere, the lower the pressure and the lower the temperature.
The earth also receives heat from the sun. However, the sun's heat does not directly heat the earth's air. The sun heats the ground once, and then the air is heated by the heat of the reflected heat. In other words, the atmosphere warms up from the bottom, which is closer to the ground.
On top of a mountain, the air pressure is lower, so the temperature drops. Moreover, since the air warms up from the bottom, it is colder on top of the mountain in any case.