It's not the same. Aircon always makes you feel uncomfortable even though a room thermometer might measure the same temperature as when you're in cold weather. Aircon will make you feel not necessarily colder too, just plain uncomfortable. You've probably experienced it before, or maybe you haven't and this is the first time you're hearing of it. But I'll you why. Aircon is just too artificial compared to a natural cold weather.
Firstly, cold air from air conditioning is blown out through a small outlet. Even the biggest industrial air conditioning units are still tiny compared to the vast open air of mother nature that extends thousands of meters skyward. This means that you're having only one source of cold air, and a very small one too.
Now, your room that you're trying to cool is probably several hundred to several ten thousand times the size of that small outlet that the air is coming from. How the hell is it gonna cool the room let's say to the preset of 20°C? By blowing out air colder than it of course. So now, your air conditioning isn't exactly obeying you to make the room 20°C. Sure, the average temperature might be, or rather, the temperature at the SENSOR is probably at 20°C, but the rest of the room is another matter. There's gonna be uneven temperature distribution all over the place, not only generally, but I'd also bet that because the air coming from the outlet is produced by a fan, it's not laminar. Non-laminar airflow creates lots of turbulance and thus an even greater uneven temperature distribution.
The more avenues your room has to let heat in, the more uneven the temperature distribution is going to be. Most rooms have windows, and that's a big source of heat more than you think. It's the thinnest wall of the room firstly, and secondly, it allows sunlight in. That sunlight is not only heating up the glass of the window, but those rays that pass through will heat up anything they hit, which could be the wall opposite the window at certain times of the day, or maybe the floor in the middle of the room. All this heating has to be neutralised, but your tiny air conditioning unit (comparatively) can't do anything about it apart from causing greater disparity between the temperatures in the process of attempting to.
See where I'm going? Nature provides this big fridge naturally during cold weather that has more or less even temperature over small distances (centimetres to metres), and gradual changes in temperature over larger distances (metres to kilometres), which when brought into human perspective means that you can't feel the difference in temperature between your right arm and left arm in a naturally cold environment, whereas you could feel the difference in temperature between your head and your feet in an air conditioned environment in some cases. In most cases, all you need is to walk across the room to feel the difference in temperature.
Human beings don't take too kindly to temperature changes. It screws up our biological function. I mean, come on, we're warm-blooded, with systems to release additional heat, and systems to produce more heat. That probably tells you enough.
So think about it before you ever make such a statement as, "I thought you liked cold weather!" when talking to someone who's lamenting about how cold the room is because of the air conditioning, or how uncomfortable that person is because of the air conditioning.