I tested your code and it works with a few changes...

1. Make sure that the texture you are modifying was originally imported with Read/Write enabled (under advanced settings in the Inspector).
2. Be sure to call texture.Apply().

Here's an example showing the modifications I made...

//----------------------------------------------------------- using UnityEngine;

public class DrawLine : MonoBehaviour { public Texture2D MyTexture;

// Use this for initialization
void Start () 
{

    Draw(0, 0, 100, 100);
    renderer.material.mainTexture = MyTexture;
}

// Update is called once per frame
void Update () 
{

}

void Draw(float x1, float y1, float x2, float y2)
{
    float x,y;
    float dy = y2-y1;    
    float dx = x2-x1;    
    float m = dy/dx; 
    float dy_inc = -1;    

    if(  dy < 0 ) 
        dy = 1;    

    float dx_inc = 1;    
    if(  dx < 0 ) 
        dx = -1; 

    if( Mathf.Abs(dy) > Mathf.Abs(dx) )
    {
        for( y = y2; y < y1; y += dy_inc )
        {                
            x = x1 + ( y - y1 ) * m;
            Debug.Log("Setting Pixel at: x=" + x + ", y=" + y);
            MyTexture.SetPixel((int)(x), (int)(y), Color.black);       
        }
    }
    else
    {
        for( x = x1; x < x2; x +=  dx_inc  ) 
        {
            y = y1 + ( x - x1 ) * m;
            Debug.Log("Setting Pixel at: x=" + x + ", y=" + y);
            MyTexture.SetPixel((int)(x), (int)(y), Color.black);           
        }
    }
    MyTexture.Apply();
}

}