So, the question* was do only cool people wear trench coats or are they cool because they wear a trench coat? I wrote down the first 10 characters I could think of who always/often wear the mighty trench, and I have to admit, most of them are pretty awesome.
1. Rorschach

2. Paladin Anderson

3. Bigby Wolf

4. Inspector Gadget

5. Castiel

6. Conner MacLeod of the Clan Macleod

7. The Crow

8. Beetlejuice

9. Gambit

10. Gally (and Ido)

*The Question gets honorable mention too. As does Nny.
1. Rorschach

2. Paladin Anderson

3. Bigby Wolf

4. Inspector Gadget

5. Castiel

6. Conner MacLeod of the Clan Macleod

7. The Crow

8. Beetlejuice

9. Gambit

10. Gally (and Ido)

*The Question gets honorable mention too. As does Nny.