Here's the thing about the cool weather being good for fat burning. It has to be REAL cold, enough that you are feeling cold even while training. Then, your body has to burn extra calories to keep warm. But if the exercise is enough to warm you up, then your body won't need to burn ADDITIONAL calories to keep warm, the workout is doing it. This is why cyclists who are riding for 6 hours in the mountains bonk if they don't eat extra food on colder days--their bodies are burning extra calories to keep warm, especially because the wind from biking at high speeds can chill you.
But the most important thing is the actual exercise. DO NOT back off the intensity or do less just so you can stay cold--the actual calories burned to warm up the body aren't that high.
One question I have about this theory is, how come Africans and Asians (who live in warm climates) are relatively lean, while the Eskimos are more chubby?