Trying to fix a drafty Door...

So I am not a hundred percent sure if this is the right flair or not but here we go. So my trailer is from 1997 (may be even a few years older) and the doors have a pretty big gap especially now that mom has ripped all the carpet out a few years back. This hadn't been an issue until recently. I finally was able to get a dedicated outlet for my window AC that stopped us throwing a breaker every time I fired it up. But I am losing a lot of cold air out of here to the rest of the house through my 3" door gap. I asked mom why the door gap was so dang prominent and she said the repair folks who did the flooring etc said it was to help with ventilation or something like that.

Well the crux of my question is, how can I close that gap without rendering the door unable to open/close and without scraping her flooring to hell and back. I thought I was going to be smart and get a thing that hugs the bottom of the door but they are for under 1" gaps and mine apparently is abnormally large for a door gap. Any ideas or suggestions would be extremely helpful :)