You could technically serialize the Texture2D via a stream and send a Byte Array over the network. Then deserialize the data on the other end. This might be useful on something like a dedicated server with special pictures or custom maps that you want to pass to everyone without making them go get them somewhere. For the record, in your case I agree that seed is the way to go, if for no other reason than because you're lucky enough to have that options, and sending an int is much easier than a byte array. That being said, try something like this:
Texture2D image = Content.Load<Texture2D>("test"); //Or rather however you ended up making your texture
MemoryStream stream = new MemoryStream();
image.SaveAsJpeg(stream, image.Width, image.Height);
byte[] data = stream.ToArray();
Then you can pass data over the network and deserialize it on the other side.