As long as the flow stagnates via a steady, adiabatic process with no external work. Yes it can be confusing. But it doesn't get hot and cold in the same place. For more on this read the discussion from the T10 mud responses. Yes it is fair logic if your T is the stagnation temperature.
Stagnation temperature is the conserved quantity.
Because the rate of heat loss from you body is faster, it feels colder. Still unclear on the stagnation temperature problems. If they make sense when explained then you are halfway there. Work the homework problems. If still unclear, please contact, me or a TA and we can spend some more time talking about it.