Introduction: Brown adipose tissue (BAT) serves to produce heat by nonshivering thermogenesis. Activation of BAT increases energy expenditure and is seen as a putative strategy to treat obesity. There are conflicting data on the capacity for cold-induced thermogenesis in individuals with higher BMI. Methods: To investigate the effect of BMI on cold-induced stimulation of energy expenditure, changes in the metabolic profile, and the expression of browning markers in subcutaneous white adipose tissue (scWAT), healthy adults (N = 173, 50.9% females) with a median age of 26.0 (interquartile range [IQR]: 23.0; 28.0) years and a median body mass index (BMI) of 23.6 [IQR: 21.9; 26.6] kg/m<sup>2</sup> were exposed to short-term mild cold exposure (CE). Resting energy expenditure (REE) was measured by indirect calorimetry and blood sampling was conducted at baseline and after CE. In a subgroup of participants with obesity, subcutaneous abdominal fat biopsies were taken before and after CE. Results: The cold-induced median increase in REE was 74 (IQR: −28; 241) kcal/day (p < 0.001). This increase negatively correlated with BMI (p < 0.001). Participants with BMI 18.5–24.9 kg/m<sup>2</sup> displayed a significant median increase of 103 kcal/day (p < 0.001), participants with overweight or obesity were not able to increase REE (23, p = 0.468 or −30 kcal/day, p = 0.917, respectively). In participants with obesity, expression of cell death activator in scWAT after CE was upregulated in females (p = 0.034). Conclusions: Persons with overweight and obesity do not increase REE in response to CE, presumably reflecting lower BAT activity. Likewise, the metabolic response to cold is diminished in participants with elevated BMI.