Dave already provided the scientific source that does confirm that men use up more energy when staying in a colder environment.
Nevertheless, your question puts this question into the specific context of a diet or losing weight and i feel that Dave's answer is missing this context.
At 16°C (EB), EE (total 24 h EE) was increased to 12.9±2.0 MJ/day as
compared to 12.2±2.2 MJ/day at 22°C (P<0.01)
The difference is comparingly small and a diet using this technique alone will most likely not lead to the desired effect of losing weight. The average energy that is being consumed by being six degress colder is less than 1 MJ/day. This equals a maximum of 238.85 calories which is less than one ball of vanilla ice cream.
Personally, i'd rather have 238 calories more while being 6°C warmer.