An Elementary Question on Sampling (Apologies if the question is too basic or vague. I have taken only one course in the subject long ago. This question stems from a silly argument I was having with a friend)
Two friends want to find out the temperature below which a given population of people would consider the weather to be 'cold'. 
If they are given a table such as:
$$\begin{matrix} 
X & | & 0 & 1 & 1 & 1 & & 0 & \ldots \\ 
T (^\circ C) & | & 20 & -10 & 7 & -15 & & 25 & \ldots
\end{matrix}$$
Where $X$ stands for the binary response of Cold (1) and Not Cold (0) one could perform a Logistic Regression to find the threshold temperature. 

How would one go about filling such a table? Does one randomly select a number of people and ask their opinion on randomly selected temperatures? 
Or 
The above is completely wrong headed and instead the following sort of procedure is more true to real research: 

We randomly select a number of people and quiz them on a complete range of temperatures to create a following sort of frequency table:
$$\begin{matrix} 
\text{Temp Range} & | & -10 \sim -5 & -5 \sim 0 & 0 \sim 5 & 5 \sim 10 & 10 \sim 15 & \ldots \\ 
\text{Answered 'Not Cold'} & | & 2 & 4 & 7 & 10 & 60 & \ldots
\end{matrix}$$
This table gives a distribution $F$. We fix on a fraction we'll consider a minority, say $\theta = 0.1$ and consider a value $m_F ^\circ C$ such that $P(F \lt m_F) = \theta$  i.e. $1-\theta$ (in this case $0.9$) of the population finds temperature at and above this value to be 'Not Cold' and decide that for temperatures less than $m_F$ 'the population' will find the temperature cold i.e. $m_F$ will be the answer we are looking for. 
 A: If you just want to know below which temperature a population of people are feeling cold, it looks like you are more looking for descriptive statistics https://en.wikipedia.org/wiki/Descriptive_statistics rather than for any analysis. The best way to answer your question is to make sure that you collect a large enough sample of people randomly chosen in the population you want to study. Such sampling questions are often discussed in social sciences, see for example: Frankfort-Nachmias, Chava, and David Nachmias. Study guide for research methods in the social sciences. Macmillan, 2007.
The best way to collect such data would probably be to decrease the temperature in a room and record the temperature at which people start feeling cold or warm. You would ideally not tell them that this study is about the room temperature if this complies with the ethical standards of your country and lab.
You could then use the average or median temperature at which people start feeling cold to describe your population, and could fit a logistic regression on the temperature at which people start feeling cold. This would be challenging if you use a range (categorical variable), especially since you do not have a clear hypothesis to test. From this logistic regression you could infer the inflection point, but it is most likely to be the same as the average or the median.
To sum up: a nice figure and calculating the average or the median is probably what you are looking for.
