I would count it.

Really, it is all about what your definition is and what your goals are. In your case, the "breaks" you had were not that long and they were not of any real benefit, given the fact that you were freezing, they probably hindered you.

I generally count my "rides" as anything ridden during the same day and day is midnight to midnight. However, I can not remember the last time I had a significant break in a ride even something as long as a lunch stop. But I did use to go to morning club rides and evening club rides and I just combined the mileage.

However, I do not approve of riding in the afternoon and then early the next morning to sleeze in a century.