Much the same as for yellow stars. The habitable zone inner edge would be high intensity, akin to the equator here so very intense bright sun, the outer edge could be twilight and barely above freezing.
Red dwarfs have a habitable zone that is both smaller and much closer than those of larger suns such as ours.
One of the problems is radiation from the sun, being much closer worlds with weaker magnetic fields would have higher radiation levels. A 0.5 G world at the very inner edge could have no ice anywhere, standing water only at the poles, salt flats round the equators, enough radiation to kill you if you step outside of a shelter without a hostile environment suit and the highest order of life could be giant semi intelligent cockroaches
One a world close to a red dwarf the northern lights would be a sign to run for those bunkers and shielded buildings.
If our sun was a red dwarf and we were still the same distance away we would live on a very dark and cold ball. We would be right at the outer edge of (or outside) the habitable zone. The sun would be a dim red glow above the clouds, there may be no unfrozen water on the surface, water existed as liquid only deep below the ice sheets.