Eric Agol has a paper about the possibility of habitable planets near white dwarf stars: http://arxiv.org/abs/1103.2791 It seems that it is possible to have planets in the habitable zone for at least 3 billion years as the dwarf slowly cools. They would have to form after the initial nova explosion as the star left the red giant stage, or be original planets that have migrated inwards due to slowing gas clouds. The "year" would be between 10-30 hours. Due to tidal forces the planet would be tidally locked with one face in constant daylight and one in constant darkness. But the rapid "year" would create Coriolis forces in the weather like the ones on Earth, allowing things like cyclones to form and move heat between the hemispheres. The star would be about the same brightness and size in the sky as the Sun. Sounds like a cool exoplanet setting.