What would the geology and climate of a supposed landmass near the pole be like, assuming a thoroughly warmer planet?
For a very basic explanation of why poles are the way they are, note that the amount of solar radiation coming from the sun is spread over a larger area at the pole. Therefore you get less radiation per square meter. As a result it is colder.

Cold air can hold less water vapour. As such it is very dry (in terms of water mass per air volume) in cold regions. Dry air obviously can provide less precipitation. If your polar continent is warmer, you'll see more precipitation.

Large-scale weather phenomena are indeed mostly driven by Earth's rotation. As such you have somewhat more stable conditions along the poles. However, complex topography (i.e. mountains) can severely interfere with these conditions. This is the reason why the stratospheric ozone hole is much smaller in the northern hemisphere than in the southern hemisphere: There is much more mixing between differnt air regions in the north. In the troposphere this effect is even more pronounced.