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Swapping the two for loops should work:

for (int x=0;x< frame_gray.cols;x+=1){
    for( int y=0; y< frame_gray.rows; y++){
        cout<<"pixel at X="<<x<<" and y="<<y<<" is: "<<frame_gray.at<uchar>(y,x);
        if (frame_gray.at<uchar>(y,x)==0)
        {  cout << " (black)" << endl;}

        else
        {  cout << " (white)" << endl;}
        //waitKey(0);

    }

    cout << "new pixel column: "<<x << endl;
}

In the meantime, as long as it's possible, you should use line-by-line processing and line pointers. It's faster than direct element access with image.at<type>(y,x).