weatherproofing hung parallel to the floor is a good idea ..

I'm no carpenter, and by no means crafty with wood. My initial thought would be, cut 2x4 same grade and type of lumber as your door a few inches longer than the door. Lay it flat on the floor against door. Place pencil line along door across top of the 2x4 or just the edges. If its right against the top of the board measure up 1/4 inch each side and take yard stick at each mark, draw straight line. Cut across the line, place 2x4 parallel with bottom of door and draw lines on 2x4 of the edges of the door (reason for the 2x to be slightly longer). Then use wood glue and some penny nails at 45 to fasten the two together. Countersink them just slightly and use some wood filler.

May want to practice the 45 nailing on a few practice pieces. Stain the door and new piece of lumber same. Or paint. The nails need to penetrate the door 1/2" or so. Careful not to break your glass in the door.

Make sure 2x4 same thickness also.

Just my first opinion, take photo to local lumberyard and get their opinion too :)

Let us know your outcome.

Get a longer door then cut it to make it appear straight when closed...
(So you would cut the door crooked on the bottom)

Only I wouldn't know if it would open all the way out.

I like the idea of photo to real lumber yard - not big box store - for advice.

You will need a soft skirt of some sort because when the door is opened anything solid will catch on the floor. You could maybe try felt strips cut on the angle of the fall of the floor, one on each side of the door so it looks like part of the door. Match the colour of the door and you will hardly notice it and it will stop any drafts as well. Good luck!

Yep, thought so, it would catch the floor...
Hmmm, if you flip the hinges to the other side( front right to left), while following my directions earlier... Would it still catch the floor??

Hmmm, nvm that, open to the left would make it awkward with that open door there to the left.
Try foot skirt like everyone has mentioned.

Duh, just cut the door at the bottom right to have an 1 inch gap like the left side. Is what I was trying to say.