Does our skin keep us warm or cools us?

All planets are warmer in the interior than on their exterior.
We know of no exception.
This also applies to stars.
In regard to planets, *can* there be exceptions?
In regards to asteroids can there be exceptions? *

On a planet where is it the coldest?

On Earth it's about 10 km up.
The same goes for Venus and other planets with significant atmospheres- somewhere around the point where about 1/2 of the mass of the atmosphere is below it.

If we were more objective we would characterize Earth by it's warmest interior temperature and coolest temperature- somewhere 10 km up. But we more practical than this and instead focus on the air temperatures where we live- and this ok, because one can simply convert this by -3 F per 1000' in elevation- and it works out roughly.

Now, with a planet without a significant atmosphere [and with planets with atmospheres] polar regions are the coldest places. One could define polar regions as regions in which the solar radiation has the lowest average angle of incidence- this applies to "level ground". Obviously mountains, or simply isolated boulders on a plain could alter the angle of this solar incidence.

On planets with atmosphere, such as Earth the angle of solar incidence is also significant due the quantity of atmosphere the radiation must pass through before hitting the surface. On worlds without an atmosphere this is obviously not a factor.

As general rule, polar regions receive more hours of sunlight per year than compared regions at the equator. And in polar regions such as on the Moon and Mercury there can be regions due to terrain features which in there is permanent shadow. Compared to equatorial regions, the surface terrain can more dramatically affect larger areas in the polar regions in regards to the number of hours of sunlight per year.

If you live in the northern hemisphere on Earth, there is similar affect which called being in a southern exposure- you get more sunlight and it's better place to grow plants. You will have more extreme examples of "southern
exposure" in polar region- and on a mountain side with "southern exposure"- one could also have a larger angle of solar incident and more hours of sunlight per year.