Is it possible to exchange textures in a ready game by upload?

Of course you can.

Uploading works like this (script from http://docs.unity3d.com/Documentation/ScriptReference/WWWForm.html )

 var screenShotURL= "http://www.my-server.com/cgi-bin/screenshot.pl";

 function UploadPNG() {
     // We should only read the screen after all rendering is complete
     yield WaitForEndOfFrame();
 
     // Create a texture the size of the screen, RGB24 format
     var width = Screen.width;
     var height = Screen.height;
     var tex = new Texture2D( width, height, TextureFormat.RGB24, false );
     // Read screen contents into the texture
     tex.ReadPixels( Rect(0, 0, width, height), 0, 0 );
     tex.Apply();
 
     // Encode texture into PNG
     var bytes = tex.EncodeToPNG();
     Destroy( tex );
 
     // Create a Web Form
     var form = new WWWForm();
     form.AddField("frameCount", Time.frameCount.ToString());
     form.AddBinaryData("fileUpload", bytes, "screenShot.png", "image/png");
 
     // Upload to a cgi script
     var w = WWW(screenShotURL, form);
     yield w;
     if (!String.IsNullOrEmpty(w.error))
         print(w.error);
     else
         print("Finished Uploading Screenshot");
 }

and downloading (from https://docs.unity3d.com/Documentation/ScriptReference/WWW-texture.html ):

 function DownloadPNG () 
 {
      // Start a download of the given URL
     var www : WWW = new WWW (screenShotURL);

     // Wait for download to complete
     yield www;

     // assign texture
     renderer.material.mainTexture = www.texture;
 }