Convert transparent png in color to single color

If the image doesn't use alpha channel for transparency then the following will do:

Bitmap image;

for (int x = 0; x < image.Width; x++)
{
    for (int y = 0; y < image.Height; y++)
    {
        if (image.GetPixel(x, y) != Color.Transparent)
        {
            image.SetPixel(x, y, Color.White);
        }
    }
}

The other answers was helpful and got me going, thanks a lot. I couldn't make them work though, not sure why. But I also found out that I wanted to keep the original alpha value of the pixels, rendering the edges smooth. This is what I came up with.

for (int x = 0; x < bitmap.Width; x++)
{
    for (int y = 0; y < bitmap.Height; y++)
    {
        Color bitColor = bitmap.GetPixel(x, y);
        //Sets all the pixels to white but with the original alpha value
        bitmap.SetPixel(x, y, Color.FromArgb(bitColor.A, 255, 255, 255));
    }
}

Here is a screen dump of the result magnified a few times (original on top):
_{(source: codeodyssey.se)}

SetPixel is just about the slowest possible way to do that. You can use a ColorMatrix instead:

var newImage = new Bitmap(original.Width, original.Height,
                          original.PixelFormat);

using (var g = Graphics.FromImage(newImage)) {
    var matrix = new ColorMatrix(new[] {
        new float[] { 1.0f, 0.0f, 0.0f, 0.0f, 0.0f },
        new float[] { 0.0f, 1.0f, 0.0f, 0.0f, 0.0f },
        new float[] { 0.0f, 0.0f, 1.0f, 0.0f, 0.0f },
        new float[] { 0.0f, 0.0f, 0.0f, 1.0f, 0.0f },
        new float[] { 1.0f, 1.0f, 1.0f, 0.0f, 1.0f }
    });

    var attributes = new ImageAttributes();

    attributes.SetColorMatrix(matrix);

    g.DrawImage(original,
                new Rectangle(0, 0, original.Width, original.Height),
                0, 0, original.Width, original.Height,
                GraphicsUnit.Pixel, attributes);
}