You guys are confusing a lot of things and the some of the postings are filled with misinformation. The octane of a given fuel has NOTHING to do with the energy released when it is burned. Octane in non-scientific terms is the measurement of a given fuel's resistance to auto ignition. Higher octane fuel self ignites at a higher temperature. That temperature is reached by compressing the air on the compression stroke of the cylinder. One detrimental issue with the higher octane fuel is it's slower burn rate. For this reason we try to ignite it earlier in order to get it near maximum burn at just past top dead center of the power stroke.
Cold air helps get more oxygen into the cylinder with means more fuel can be introduced at WOT and more power can be developed. It also means there is more air to be compressed and a higher pre-ignition temperature inside the cylinder.
A detriment effect of cold air is it is more dense and it produces more drag on the body of the vehicle going down the road. One of the things most any pilot can tell you is it takes much less runway to get an airplane off the ground at 0 degrees than it takes at say 100 degrees. We have table for every aircraft and are suppose to calculate the effect of outside temperature prior to every take off.
Why is this? Because the engine can develop more power and the more dense air traveling across the wings develops more lift. Hense a shorter take off roll. Once off the ground the trick is to go high where that air is much thinner. Thinner air means less drag with more speed and better fuel economy. Have you ever wondered why commercial jet aircraft cruise up to the 40,000 feet range. The answer is much less drag and better fuel economy. The temperature is much colder but that is not a factor. They use an engine compressor stage to get enought air in to burn fuel at that altitude
Back to the gasoline powered engine. Since 87 octane burns quicker than 91 or 93 or 100LL, it will develop slightly more power because the piston is closer to Top Dead Center when most of the fuel is burned.
So it is a delicate balance of how soon to ignite the fuel to get the most power from without firing too soon to cause it to burn before TDC causing detonation or ignition ping. In a ground vehicle the air (and fuel) charge is seldom a full charge since we do not drive at WOT (Wide Open Throttle) continuously. With less than a full charge the mixture burns more slowly and more ignition advance can be tolerated.
Octane rating has little to do with power or mpg. As an example ethanol has a higher octane rating than gasoline but is has a lower btu per gallon rating than gasoline. So while it is higher octane it gets poorer mileage than straight gasoline.
If you want to dig into it further take a look here at the GGE (Gasoline Gallon Equivalent) tables for various fuels.
Gasoline gallon equivalent - Wikipedia, the free encyclopedia
I'll stay out of the fray, because these types of threads always bring out the urban legends, marketing hype, and the people that "know it all" about this stuff. I watched one thread go on for months on an "econo-box" forum that I watch. It got stretched into attributes of ethanol and "top tier" marketing of various brands of fuel.
Good luck on this discussion. Just do not read believe everything you read. Everyone is a expert on this subject.
Remember that they can not put anything on the Internet that isn't true.