I've seen very similar things done by some 'old school' pros, but never had the opportunity (or optimism) to attempt such a thing myself.
You won't get a paint product that will give you what you want in one.
You'll need to apply a solid base coat of an exterior paint suitable for metal to the door, in the general oak colour you want to achieve. (Probably a tan/brown in a light/medium/dark shade.)
Once dry, you can use a thin coat of a suitably darker gel stain to cover the whole door and then use a wood-graining tool to achieve the look of timber. This isn't as easy as it sounds, and will take some practice to get an acceptable look, if you've never done it before. When using the tool, use a rocking motion to achieve graining and knot effects, working in the direction you would expect a wooden door to be constructed (panels/rails/stiles), and remove any gel from the tool before moving on. Work quickly, but steadily, otherwise you'll end up with a mess - if you make a mistake when graining, immediately wipe the section off, and apply some fresh gel before continuing. Once you have got the finish you want, allow to dry and coat with either a clear oil based exterior polyurethane (water based may possibly be suitable these days) or some form of clear lacquer.
As already stated, you may end up doing a lot of preparation and work, only to end up with something that doesn't look that good. If you don't like the other options, I suppose it would be worth a go.
I hope it works for you because, even as a decorator of 20+ years, I would prefer to pass this kind of thing onto somebody else.