There are many factors that need to be considered when answering this question. The first is the weather. If you live in a region where the nights are very cold, you might want to stall your horse at night. Another thing is your horse's health. If the horse is in a good shape, without any health issues, he will be perfectly fine spending nights outdoors. Another important thing to consider is the safety of the environment, where the horse is being kept. If the area is safe and provides everything necessary (access to fresh water, pasture and possibly a shelter) there is no reason why not to keep your horse out at night as long as the other two conditions are met.