Why do people feel extreme cold at different temperatures compared to other people of same body structure?
First of all, this observation is the norm across human perception. While humans react in roughly the same way to similar stimuli (e.g. both a cranberry and a tomato are seen as red, the destruction of tissue is felt as painful), the intensity tends to be different. Also, many stimuli elicit not just a knowledge of the state of the world or one's body, but also a reaction (e.g. shivering when cold, or emotions like fear when physical pain is felt), and these reactions differ between humans too. So, on a very general level, it can be answered with "Because that's how human perception works". 

I know that this is a very unsatisfactory answer, so here are some factors off the top of my head. For any given case, one or more of them will cause the difference, and you cannot tell which ones from casual observation. 


Your observation of "similar clothing" could have been incorrect. For example, an acrylic sweater can look exactly like a sheep wool sweater, but warms much less. Or, slightly shorter sleeves can cause much cooling if they leave the wrist exposed. Layering is also very important, and we generally only notice the uppermost clothing layer. 
Your observation of "similar body structure" could have been not precise enough. People who have the same appearance can have different amounts and distributions of body fat. Maybe one person is simply better insulated than another one. 
The state of their circulatory system was different. Vasoconstriction and vasodilation will change the skin temperature, which is sensed by peripheral thermoreceptors. 
Estrogen is involved in thermal perception. The gender of the person and the current point in the menstrual cycle (or pregnancy) in women will make a difference. 
The circadian cycle of the two people is probably not perfectly synchronised. Core body temperature varies during the cycle, and thermoperception depends on core body temperature too, not just skin temperature. 
A different metabolism will cause one person to create more body heat than another
Other hormones (beyond estrogen and the ones ruling the circadian cycle and metabolism) probably have an effect on thermoperception, but I can't tell you details here. Temperature is regulated in the hypothalamic-pituitary-adrenal axis, so the hormones from it are likely to have an influence. 
Normal variations in the two people's neural networks will change the intensity of signal perception. People are born with very unconnected neurons, and build unique connections depending on the environment they encounter while growing up. As a result, each person's brain functions slightly differently when given the same input. 
Differences in neurotransmitter sensitivity can account for the difference in intensity of perception. People sometimes react differently to the same level of neurotransmitter, or also their brains secrete different amounts of neurotransmitter as a response to the same stimulus. These differences exist on an average level (e.g. glutamate can potentially "do" more for me than for you) but are also affected by drugs and illness. 
Attention is a major part of perception. The CNS can suppress information from sensory organs at a very low level if the brain is focusing elsewhere. 
Habit: people can intentionally or unintentionally learn to disregard or misinterpret their body sensations. 
Psychological stress increases the core body temperature 
The above reasons all assumed differences between a pair of healthy individuals. Some conditions, for example running a fever, but also neurological disorders anywhere along the complex pathways from sensors to cortex (and the other way round!) or diseases which for some reason alter thermoregulation, will all change the feeling of hot or cold. 


This list is probably incomplete. Also, some of the factors I listed will overlap to some extent (e.g. vasodilation is frequently mediated through hormones, and ingrained habits are reflected in neural network connections). But the take away point is: Human perception is an active process, very far removed from simple "reporting" of the state of the environment. It is unrealistic to expect two individuals to have the same perception when exposed to the same stimuli. 

For an in-depth description of how thermoperception and thermoregulation work physiologically, see this summarizing paper.