I wouldn't use that aromatic red cedar door, if I were you! Your cigars will taste like a cedar tree......the wrong kind....but you already knew that, didn't you?
(Big difference between common red cedar and Spanish cedar.) Mahogany would probably be okay, though.
To solve your problem:
All you have to do is get the rubber "sweep" that goes on the bottom of an exterior door. These usuall have 3 or 4 rubbers "fins" that seal on top of the threshold. All you'll need to do is glue it or nail it/staple it to the bottom of the door. They come in several heights, to account for doors that do not have an adjustable threshold. I'd get the tallest size, and see how it covers the space below the door.
If it isn't producing a good enough seal, then just glue/nail a strip of wood across the bottom of the door to make the gap from the bottom of the door to the floor smaller, which will allow the door "sweep" to seal nicely.
The sweeps are available at most any Home Depot or Lowes. They're pretty cheap, only a few dollars, and can be cut easily to the proper length. Since they are rubber, and designed for an exterior door, it should last a long, long time.
I would also go ahead and get some thin foam adhesive-backed weather stripping as well to take care of any leaks along the door "stop". Apply it all the way around the door where it meets the wood to produce a good seal, like an exterior door is done. This is probably going to be way cheaper and easier than installing an entire exterior door jamb.
Here's two that I found at Lowe's when I did a quick search:
(They will seal a gap up to 3/4" and are adjustable)
http://www.lowes.com/lkn?action=pro...categoryId=WEATHERSTRIPPING.CATEGORY&pad=true
Hope this helps....