As Shanon mentioned above, you may want to use exceptions instead of return codes.
Also, too many comments IMO. Too many obvious comments.
// Attempt to load the image file.
if( LoadImage( newInfo, newTexture ) == false )
The method being called is named LoadImage() so the comment is obvious. In my opinion most of the comments in that file are no more than overhead.
The switch statements on lines 121, 137 and 214 are good candidates for extracting a new method.
private int GetTextureSizeEnum(int size){ switch( info.Size ) { case 64: texSize = TEXTURE_SIZE_64; break; case 128: texSize = TEXTURE_SIZE_128; break; case 256: texSize = TEXTURE_SIZE_256; break; }}private int GetColorFlag(int colors){ switch( info.Colours ) { case 4: texColours = GL_RGB4; break; case 16: texColours = GL_RGB16; break; case 256: texColours = GL_RGB256; break; }}
You may want to add a default case and throw an exception there.
The method LoadInfo() deals with loading an info file and fills an ixTextureInfo. You may want to consider moving this method to the ixTextureInfo class.
In that light, you can also move a lot of functionality to the ixTexture class. Things like Bind(), Load(binaryData), Unload(). Most things that are pre/suffixed with "Texture" can be put in the ixTexture class.
These comments have little to do with actual C++ and more with general coding style. I hope you don't mind.