It's all about the weather...
Whether you combine man's best friend with day or night, you talk about the weather.
The phrase dog days refers to the hottest time of the year, when it's so hot outside that you'd rather lie down in the shade like a dog than do hard work. The dog in this expression may be the dog star, Sirius, which has been associated with hot weather because it rises at the same time as the sun during the hottest days of summer.
The phrase three-dog night refers to nights so cold that you'd need three dogs with you to keep you warm. This is apparently an Australian saying used to describe bitterly cold nights that are difficult to survive without at least three dogs in bed with you.
