I have held a false assumption for my entire life. Up until today I had believed that the expression "the dog days" referred to "the worst of" or maybe "the epitome of". I hadn't really thought about why I've heard the term the dog days of summer about a million times, but had never heard the dog days of winter being used in a sentence.
The Romans used to associate hot weather with the star Sirius. Sirius (the Dog star) used to rise at about the same time as the sun during the middle of summer in the northern hemisphere, and the Romans believed that this was the cause of the particularly hot weather during this time of the year. They would sacrifice a brown dog at the beginning of this time period to appease the rage of Sirius. The dog days lasted from about July 24th to August 24th.
The modern French term for this time of the year, canicule, comes from this same root. It means "little dog", again referring to Sirius the dog. Many derivations have crept down from those ancient times and can be found in many of the expressions that we use today. Due to the "procession of the equinoxes", the Dog Star no longer rises with the sun in the middle of the summer, however, this terminology has taken root in our culture.
I'm not sure which animal should be used to represent these winter days. If you have any suggestions though, I'd be more than happy to find one and sacrifice it to appease whichever god is responsible for this crappy weather. Just as long as it's not a bear or something big like that, I'd prefer something that's fairly docile.