The surface of the soil should be allowed to, almost, dry between watering. Never water with cold water but with tepid water as cold water may shock the plants. As the days shorten the plants become dormant and start to drop their leaves. At this point water sparingly until new leaves emerge in late winter.1
Try to plant in a location that enjoys dappled sun and remember to apply water fairly sparingly. Rex begonia is generally regarded as a tender plant, so remember to wait until your soil is warm and the night time temperature is well above freezing before moving outside.Ruby Slippers