Does more reflective aluminum foil make a room cooler compared to less reflective foil? Aluminum foil is said to be not absorbing light at all.
It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?
If yes, then where does unreflected light go in case of less shiny aluminum foil?
Does less shiny and more shiny actually make a difference? Why?
In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too?
 A: First, there's no perfect reflector nor absorber. In fact - even Aluminium does absorb some radiation (by which it gets heated, can be noticed at incident high frequency radiation). One more thing is that aluminium foils are designed in a way to reflect light.
Here's the Wiki article quote...

Aluminium foil has a shiny side and a matte side. The shiny side is produced when the aluminium is rolled during the final pass. It is difficult to produce rollers with a gap fine enough to cope with the foil gauge, therefore, for the final pass, two sheets are rolled at the same time, doubling the thickness of the gauge at entry to the rollers. When the sheets are later separated, the inside surface is dull, and the outside surface is shiny. This difference in the finish has led to the perception that favouring a side has an effect when cooking. While many believe that the different properties keep heat out when wrapped with the shiny finish facing out, and keep heat in with the shiny finish facing inwards, the actual difference is imperceptible without instrumentation. The reflectivity of bright aluminium foil is 88% while dull embossed foil is about 80%.

The shiny and not-shiny surfaces are totally a favor of production technology (credit goes to the rollers). Now, to the "why" question.
As a physics parameter, we use reflectivity to address the shininess. As we can see, the reflectivity is quite high for the bright surface, compared to dull one. The unreflected light (as you say) can go anywhere. It can go inside the aluminium foil (i.e) it's absorbed and hence the 12% & 20% loss...
Response to comment (based on edit): That's a nice strange idea. With some perfection (I mean, there should be very less allowance of any sorta radiation inside), the room will be relatively cooler. But, in reality (where we can't expect idealistic things), there will always be some radiation inside. But, it keeps the room warmer compared to the outside. But, always be careful when playing with such things because, any sort of harmful radiation (if any- what about a heater or even an electric iron?) inside the room will be reflected back to you by the matte side - which can be very harmful...
A: It depends where the aluminum foil is situated.
For example I use aluminum foil behind a wood stove to reflect the heat to the room instead of heating the wall.

So, does it mean that a more shiny aluminium foil will reflect more light and thus make the room more cooler as compared to less shiny foil?

You can see from Crazy Buddy's answer that the more mirror like the surface the less is absorbed by the foil.

If yes, then where does unreflected light go in case of less shiny aluminium foil?

The unreflected light is absorbed and ends up in heating the foil itself.
Thus, if you have an aluminum foil on a sun side of a wall you have to leave air between the wall and the aluminum so as not to get that residual heat heat the wall by contact. Air is a bad conductor of heat.
You could have it on an inside wall if you want to reflect back all the energy and have few heat losses. Again an air gap will help keeping the heat in the room instead of heating the wall and radiating energy out.
