I am going to use Foam insulation in a box to help keep temps at a good fermenting temperature, the foam has a alumunum foil on one side and white foam on the other. Which side should the foil be facing, should the "foil" be facing to the inside where yo can see it when you open the box or turned around so the "white foam" side faces the inside of the cold box?

The foam will also act as a vapor barrier and since this will be colder than room temp, I'd put it on the outside like what is done with walk-in coolers. Just my suggestion.

When put on a house, the foam board you are referring to is installed with the foil oriented to the outside of the house, immediately under the siding. I have been told it is supposed to reflect some of the heat away, but I have no credible evidence that one way really works better than the other.

I can only tell you for sure that the vapor barrier on a cold room needs to be on the outside, which is backwards to what is on a house.

I'm not sure how the bare Styrofoam side is more of a vapor barrier than the foil side, but I am not here to argue. I honestly don't think the difference is substantial enough either way with foam board material around a small container.

foil to outside, yes it makes a difference.....

I'd put the foil on the outside and then I wrap the whole thing in a good heavy plastic with the seams sealed with tape.

but...wouldnt the foil get colder faster then the white side, so if this would be right shouldn't it be facing the inside where it would help keep things cold? Am i overthinking this?

the foil is a radiant barrier and reflects the heat. You can do the same to your attic.

I put that in my attic and it helped. When ever we replace the roof, I'm putting the foil faced felt ( say that quickly three times) under the shingles.