Below is a terrestrial planet with an axial tilt of 58°. As a consequence of this the polar circles (32° N&S) are closer to the equator than the poles, and the tropic circles (58° N&S) are closer to the poles than the equator:
Each pole takes turns pointed toward and away from the sun for about half the year, as on Earth, but because the tilt here is more than twice that of Earth the winter freeze actually extends to and beyond the equator, to the summer half of the planet (depending on geography – on Earth Arctic sea ice can reach as far south as 45°N and Antarctic sea ice as far north as 20°S).
This planet is also farther from its sun than Earth so it receives less energy, has a thinner atmosphere, which retains less heat and produces less of a greenhouse effect, and may also have a shorter year and day than Earth. By combining some of these variations it's likely snow and sea ice dominate the landscape for most of the year for most of the equatorial region, and it's entirely possible winter snow and ice could be found year-round.
Note: This assumes a planet with significant land in the area of the poles. Climate at high obliquity (PDF) concludes (in section 6. 188
Conclusion and Appendix A) that an ocean world with axial tilt of 54°-90° would largely remain above freezing thanks to the thermal transport properties of the oceans:
Our simulations employ a configuration without any land. Although it reproduces (at 23.5° obliquity) the main features of present day climate, it is plausible that particular continental configurations would have a first order impact on the climate, for example in cases where large areas of land are removed from all oceanic influences (e.g. a large polar continent). In such cases, only the atmospheric heat transport could modulate the extreme seasonal fluctuations, possibly resulting in temperature excursions beyond the habitability range.
For a cold-adapted species the most habitable area of this would would be roughly 32°N–32°S, extending poleward in the winter and as local geography (such as elevation) allows. 867