You can do it through the door, but the wire is most exposed there. No the door does not shut on the wire if done correctly. But it is still closer to the elements than it would be otherwise (a hole in the firewall). Truthfully I would not worry about it unless you are looking to compete.

On my old nova i ran it thru the huge grommet on the passenger side of the car, and i pulled up all the plastic trim on the doors and pulled the carpet up and slid it in. Then i just pulled the backseat off, and ran the wire under there, but I did not install the amp in the trunk. I installed it on the vertical area between the seat and the floor. It'* right behind where your legs are, and all the cables came out 1.5-2" from their hookups. Looks very nice!