Bottom-line: colder ambient temperature does allow you to burn more calories. Whether you actually do it, is another question. E.g. in cold conditions, you may not excercise at maximum power for fear of getting really cold if you have to stop for some reason when moist of sweat.
Please note that it is not completely clear what "the same exercise" is:
- the same physical (mechanical) work over the same time (ergometer excercise - but I guess there the temperature is rather constant)
this burns more calories in heat
- the same excercise means that you are at the same percentage of your maximum physical power that you can perform. That would e.g. roughly be % max. heart beat.
No direct evidence from the literature, but the educated guess is that this scenario is between 1. and 3., and probably close to zero effect
- the same physical (mechanical) work (e.g. running the same trail), but not enforcing the same time.
this burns less calories in heat, and it is most likely what will happen in outdoor excercise practice.
However, the more or less is in the order of magnitude of $\pm$ half a minute over 30 min excercise (for elite cyclists). In other words, add another minute for every hour of excercise, and you have the same effect. If your excercise happens to be cycling, wind speed will do more.
One important consideration is that the efficency of muscles to make mechanical work isn't that high. Wikipedia says 18 - 26%, the papers below measure about 20% for cycling. That means that about 3 - 4 x the amount of energy that goes into mechanical work is heat that the body needs to get rid of. Both are burned calories.
The effect of ambient temperature on gross-efficiency in cycling found that gross efficiency decreases with high ambient temperature. These experiments were done in fashion 1: at high temperatures the cyclists needed more breathing. Skin temp went up, so did body temp. Muscle temperature was even higher, but it was not measured at the "low" temperature. Bottomline is: the body needs to work actively to get rid of the excess heat. That means, lots of blood must flow through the skin where it can cool. As they enforce mechanic output, heart beat and respiratory rates need to go up to compensate for that.
Effects of heat stress on physiological responses and exercise performance in elite cyclists. Tatterson AJ, Hahn AG, Martin DT, Febbraio MA., abstract only: paper behind paywall did another experiment: the exercise was "the same" in the sense that the cycling distance was the same. They find (and so seem to do other papers that I cannot access neither) that the mechanical power is limited by body temperature, and is actually limited in advance. So in order not to exceed the heat dissipation capacity, the mechanical work is reduced.
At the end of the first paper, the authors estimate that the lower efficiency can explain only about half of the time difference in hot vs. cool ambient temp observed in the second paper. In other words, the increased energy consumption for increased total and skin blood flow for the cooling is overcompensated by reduced mechanical output. They cite that different studies found power output decreased about 6.5% in the hot vs. moderate setting.
Note that these studies IMHO have quite high "cool" temperatures of 15 to 23 °C (hot is in the range of 32 - 35°C; but one needs to take into account the humidity as well.)
Thoughts about cold conditions:
shivering: I'd not consider shivering in the context of excercise.
longer periods (few weeks) of cold, particularly cold air in the face, trigger increased base metabolic rate (acclimatization). As far as I know, most of this is still produced by muscles. Brown fat, however, is discussed as well (but we humans don't have much of that). (Unfortunately can't find again where I read this - can anyone help, please?)
In both cases muscle work without gross movement is induced by the body in order to use the 80% of the burned calories that are dissipated as heat. When you excercise in cold weather and wear anything that can be called sensible clothes, the excess heat from the mechanic excercise is still more than enough. If it is really cold (say, below -25 or -30 °C) mouth breathing is not a good idea as the nose is needed for heat exchange and moistening of the air. Then of course the breathing puts a limit.
Experimental/anecdotical: I've been cross-country skiing in shorts and T-shirt at ca. -10°C, and did not get cold. I've also been running at -20°C in T-shirt + thin long sleeve fleece pullover and at the end there was frost at the back of the fleece: even though I did not get wet, I did sweat, thus obviously had excess heat. But then, these are not the preferred temperatures for cycling studies...