We are replacing our front door and I am wanting to freshen up our storm door which is still in great shape. I want to paint it the color of our shutters. I was going to us steel wool to clean it and spray paint to paint it. Can I do this? It is aluminum.

Is it painted now, or is it bare aluminum? Another question which you might not be able to answer: if it's bare aluminum, is it anodized, hard-color anodized, or mill finish? If it's bare and somewhat pitted, and a dark grey color, it's probably mill finish. If it's very smooth and somewhat shiny, with some feeling of depth to the surface, it's probably anodized. If it is a bronze color, can be anywhere from light to dark, it's probably hard-color anodized. Its surface would also be smooth.

Unless you have a HVLP spray gun there's little chance or an even finish, also most spray pants use oil based paint. Aluminum needs to be painted with Acrilic Latex and only then if there's already a finish on it. It would need to be cleaned and lightly sanded with 110 grit sand paper for any chance of paint sticking to it. Use a foam roller.
If it's bare aluminum then there's a long procces to etch it, seal it, prime it and then paint it.
Steel wool will never give enough "tooth" for paint to stick, if it's unfinished all you will do is expose more aluminum to the air and the patina will come back faster because the aluminum will just oxidize to protect it's self.
If this door is exposed to direct sun light never paint it a dark color. It will distroy any paint and will make a solor panel between the storm door and the inside door and will so ruin the inside door.