Most magnetic reed switches have quite low current ratings. The majority are also normally open, closing when the magnet is brought near, so you'd have the light turning on when the door closes rather than turning off. Both these problems could be overcome with an auxiliary circuit--a suitably rated mosfet controlled by the reed switch would be one rather simple and effective setup.
I did recently come across
these really nice-looking reed switches which include a normally closed one rated for up to 0.5A. That would be fine for a LED or other light of up to about 6W (assuming a 12V system).