The question was to change dynamically the Up Home Indicator, although this answer was accepting and it is about Themes and Styles. I found a way to do this programmatically, according to Adneal's answer which gives me the clue and specially the right way to do. I used the below snippet code and it works well on (tested) devices with APIs mentioned here.
For lower APIs, I use R.id.up which is not available on higher API. That's why, I retrieve this id by a little workaround which is getting the parent of home button (android.R.id.home) and its first child (android.R.id.up):  
if(Build.VERSION.SDK_INT >= Build.VERSION_CODES.ICE_CREAM_SANDWICH) {
    // get the parent view of home (app icon) imageview
    ViewGroup home = (ViewGroup) findViewById(android.R.id.home).getParent();
    // get the first child (up imageview)
    ( (ImageView) home.getChildAt(0) )
        // change the icon according to your needs
        .setImageResource(R.drawable.custom_icon_up));
} else {
    // get the up imageview directly with R.id.up
    ( (ImageView) findViewById(R.id.up) )
        .setImageResource(R.drawable.custom_icon_up));
} 
Note: If you don't use the SDK condition, you will get some NullPointerException.