Photoperiod is the trigger, so the rut happens at the same time every year. Whether or not the animals are actively moving about in daylight, however, is seriously affected by the weather. Heat is not good for an animal that has a coat that would allow it to sleep outside at the possible -10C that can easily happen at this time of year. If you dress yourself up in clothing warm enough to just lie down and sleep all night at such temperatures, and then proceeded to walk, trot, run up and down hills, get into fights, and have ### all day long, you would find yourself pretty uncomfortable.
I think in warm temperatures the animals try to limit their activity during the heat of the day and look for cool, shaded areas to help keep them cool, and maybe become more nocturnal to help with controlling body temperatures as well. As was mentioned too, they don't need as much food to keep warm either. The visible activity declines in good weather as far as hunters are concerned, but the rut happens the same time every year whether we see it or not.