@Anastasis is the wood rotten or just discolored? If it's rotten, then it will indeed suck. If it's just discolored, you can spray it with a bleach / water mixture (or a mold / mildew treatment from Lowe's / HD) and cover it back up. Do you think water is just getting in around the door itself, or do you see evidence of water intrusion around the jamb or under the threshold?
Also, what kind of exterior is around that door (siding / brick / stone / stucco) and does it have trim? When there are thresholds involved or water appears to be getting in from areas other than the weatherstripping, I'm a big fan of removing a door completely and re-setting on a proper sill pan with a silicone back dam if exterior conditions allow it. Even if you don't opt for an aluminum sill pan, a soft pan using a high-grade water barrier system (Dupont Flex Wrap is great) will provide a much better barrier than a threshold sitting on a foundation of plywood subfloor. The ideal situation is exterior trim that can be removed and reinstalled which would allow you to remove the door completely, install a sill pan, the re-set the door and properly waterproof the sides and top. If you have brick / stucco / stone it gets more complicated.
And, I agree with the above that, for retrofit applications, PVC trim is great for exterior use. Also, make sure you use a very high grade 100% silicone (NP1, Dap Dynaflex) at the transitions, and pre-fill any screw holes with the same silicone before fastening.