There are two main ways that a house (or indeed any other object) exchanges heat with its surroundings: convection and radiation. As a general rule, at everyday temperatures convection is faster than radiation so it's the dominant mode of heat transfer.
With convection it doesn't matter what colour you paint your house. Convection heating and cooling is mostly by the wind blowing against the house walls and exchanging heat with the walls by conduction. In particular at night when it's cold the house will lose heat at the same rate whether it's painted white, black or yellow with green spots.
But the radiation from sunlight has a temperature of about 5,700°C so it is very good at transporting heat, as indeed you can tell just by standing in sunlight for a few minutes. Painting your house white (or better still silver) will reduce the absorptivity because it reflects away a large proportion of the sunlight, so it will reduce the rate of heating by the sunlight while not affecting convection.
So painting your house white will reduce the amount it heats up during the day but will not affect the amount it cools down at night. The end result is that it will keep the house cooler.
In winter the sunlight is often very weak or it's cloudy, in which case convection dominates and the colour of the paint has little effect on the internal temperature. It's true that on the rare sunny days in winter the white paint will reduce how fast the house heats up, but in hot climates this is a price worth paying for keeping the house cool in the summer. I suppose ideally you'd repainting the house twice a year so it was white during the summer and black during the winter.
