I'm interested in developing a world that has somewhat extreme seasonal changes (hot, but liveable summers and cold, but livable winter) with a very cold non-habitable polar regions. Would axial tilt alone solve this problem? So for instance, if I have it a tilt of 30° I could make the seasons more extreme, but how do I account for the non-habitable polar regions?
How does Earth not meet your specifications?
First off, no one lives in Antarctica, barely anyone lives in Greenland, the Canadian Arctic, or Siberia, and even if there was land over the Arctic Sea, no one would live there. So the poles of our planet are pretty inhospitable.
Secondly, there are some pretty extreme climates about. Central Asia is a great place to look for them.
- Mazar-i-Sharif, Afghanistan has an average summer high temp of 38.9 C and a winter low of -2.1 C. The record temps go from 48.1 C to -22.3 C
- Kyzylorda, Kazakhstan has an average summer high temp of 34.3 C and a winter low of -10.3 C; the records go from 46.0 C to -33 C.
- Urumqi, China has an average summer high temp of 30.1 C and a winter low of -16.6 C; records are 41.0 C to -41.5 C.
- Kyzyl, Russia has an average summer high of 27.6 C and a low of -22.6; records from 40.7 C to -54.0 C.
Kyzyl is pretty extreme and uncomfortable, especially in the winter, yet still has 100,000 residents. You can assume that there are even less comfortable places nearby that don't have cities of 100,000. How much more extreme do you want?
Water has huge heat capacity, this means that seas and oceans absorb energy in the summer, cooling nearby areas, and release energy in the winter, heating nearby areas. They stabilise temperature, both on yearly and daily scales.
Areas very far away from large water bodies experience larger amplitudes due to lack of stabilising heat reservoir.
That's it. If your planet is more land than water, then most of the area will be subject to dry continental climate with high temperature amplitudes and low precipitation. Be ready to have a lot of steppes, deserts and other arid biomes. Perhaps large parts are genuinely uninhabitable.