Q:

Seasons & days with steep axial tilt?

Given tilt of about 90deg (like Uranus), with day & year like Venus (day longer than year), orbiting a purple (brown) dwarf (not tidal locked). I'm having trouble getting "seasons" & day length sorted. I picture seasons of "hot sunny", "cold sunny", "hot dark", & "cold dark". What would the seasons & "days" actually look like? Am I right one hemisphere's always dark?

A:

Welcome to Worldbuilding.
Viewed from either pole the sun would be directly overhead in mid-summer. Over the following 3 month period the sun would sink towards the horizon and set. 6 months of darkness would follow and the sun would then rise and over the next 3 months would climb to be directly overhead again. Decreasing the length of the day would curve the path of the sun across the sky changing the direction in which the sun would rise and set.
From the equator at mid-summer the sun would appear on the horizon and over the next 3 months would climb higher in the sky. At the autumn equinox the sun would be directly overhead. Over the next 3 months the sun would sink and disappear below the horizon for 6 months. Decreasing the length of the day would curve the path of the sun across the sky changing the direction in which the sun would rise and set.
No part of the planet would be in permeant darkness (ignoring surface relief and assuming a circular orbit and 90 degree axial tilt). This is because angular momentum is conserved so if the north pole faces the sun in the summer illuminating the northern hemisphere, the south pole must face the sun in the winter and illuminate the southern hemisphere. 
In summary 6 months of cold dark winter followed by roughly 2 months of “spring” with the sun low in the sky, 2 months of “summer” with the sun high in the sky and 2 months of “autumn” as the sun moved higher and then lower in the sky. A similar seasonal picture would be seen anywhere on the planet but the phases of the seasons would differ. 
Depending on the exact arrangement very large temperature fluctuations might be expected as the sun would either be visible or not for 6 month periods. Winters would be similar to Antarctic winters. There is no Earthly equivalent of this type of summer as in Antarctic summers the sun is always low in the sky never directly overhead.

