I am a first year PhD student. I am doing it from an institute in a remote part of the world where the temperature is -10 degrees most time of the year. I took this opportunity after doing my Masters in Europe and I was really happy with the time I spent during my masters thesis research and really liked my research and came up with good results and very good grades. Now, I have taken this scholarship position but I am already in dark. As said, this institute is in a very small town. I can't speak the language of local people. I can't go out for a walk because its too cold.
I don't think that the project is difficult. In fact it is easier for me. But my daily life is not perfect because to read a research paper or write an article I need a fresh and happy mind, which in this city and cold temperature is not possible. I have money just for food and living and no more for even traveling to another city.
Can someone please tell me if I should leave this program?
It's impossible to advise you what to do. But I would consider to give it more time, e.g., a year, before quitting. You may still be effected psychologically by the change of place, weather, geography and location; you are still not adjusted to the new place. So you feel anxious and perhaps panic. But it may not be a good strategy to haphazardly decide on quitting the PhD while in this position. So I would advise you to wait more time and see if you adjust to your place and perhaps start enjoying your project.
(Also, PhD is never easy, and so mild depression while completing a phd is quite common.)