You could certainly write something to do this in C#, but there is nothing coded directly to do this in HG. The alternative would be to have a simple C# code that checks during certain times of the day at a certain interval (every 30 minutes between sunset and sunrise) and then notifies you if the door is open. If so, then you can use the Android/Windows Phone/Web interface to close the door.
The one thing I would be cautious of with garage door control is that these are big heavy doors that can cause a lot of damage. I know automating them sounds very convenient, but safety and property damage could be at stake. If I were going to incorporate a garage door automation into my home, I would seriously consider installing a camera that could show if there were obstructions prior to blindly (essentially) closing the door. If I ever get cameras installed, this is likely something I will do since we have forgotten to close the door (or it decided to not close) when leaving the house.