TRIGGER,
Yes, deer have two different coats per year; a summer coat and a winter coat. The reddish summer coat is made of shorter, finer hairs. The grey winter coat is only about half as dense as the summer coat, but the hairs are much longer and are hollow. Retaining body heat is all about trapping air near the skin, and these hollow winter hairs work like the hollofill insulated clothing sold years ago (made with hollow fibers).
In fall, deer are genetically driven to put on body fat for winter. This fat deposition is biologically manditory and will be done even at the expanse of other body needs (and the reason acorns are so important to deer in fall--they are high in fat). Once deer have put on their winter coat (usually occurs in early September) and loaded their body with fat layers, running around in hot weather can be deadly to them. They do not have the same ability we humans do for cooling through sweating (they primarily cool themselves by panting like a dog). Due to the risks of over-heating, running long distances, like which occurs during the rut, could literally be deadly to deer in hot weather.
Although reduced daylight activity in warmer weather and increased activity in cooler weather isn't an absolute, it is the trend. If you look at hunter observations of deer (and especially bucks) over a long period of time, you will find that, on average, deer/buck sightings are higher when the weather is cooler, and lower when the weather is warmer.
Below is a graph of buck observation rates by hunters, for only the month of November, and only for morning hunts based on the low temperature for that day. Notice how data is scattered all over the place, with high and low data points for all different morning low temperatures. But the
trend (the straight line), shows declining buck observation rates with warmer morning low temperatures. In fact, buck sighting rates average only half of what they are for the warmest mornings versus the coldest mornings, on average. Yet the fact that data points are scattered all over is probably why you haven't personally observed any significant pattern in your own hunting. These type of trends require averaging a huge amount of data to see. The below data is 25 years of observations from a single property and literally involve thousands of treestand hours of observation time.