Shit, that question is really good, let me think XD.
Taking into account one month (30 days) - 3 people - 10 days each person. Food for 1 month wood mean that it also includes water or that there is water in the cavern if not all this would be useless.
First of all i would kill one of the two people, i assume you let me choose, so it would be one i don't care about and the other one is my cousin, so we have more time. It would be like 5 days more of food. Then i would use the meat from the body to have one day of food becuase then it will rot (more or less 36 days of food). Then i will try to get water from the cavern if there is some.
I would choose the desert becuase its less agressive than the snowy montain, or at least in general it is. Moreover, there are only 5 vast deserts in the world. So its much easier to identify, and by peeing in a cloth and put it on your head you can feel cold and resist the heat (so i do not get easily dehydrated). I would try to get books that are not musty so i can use the paper for the nights in the desert, in order to insulate my body from the cold and some for fire. Luckily my cousin is right handed and i am left handed so we can walk beside each other and therefore walk in a straight line.
I would also try to make use of the items in the first door, if not bad luck xD.
Well now, depending on what desert it is i would have to take X direction, if i confused of desert i would be screwed.Then be pacient and walk try to survive, defend myself from animals (can be also used as food =P), luckily i'm not alone, so its half the work.
Sorry for the long answer but i liked that question xD. I could continue but it will be too long.
What would you do if you are in the middle of a fire, inside a hotel for example (or a huge building), you cannot jump because you are in the 7th floor. Take into account that each door and window you open stokes the fire. And the vents are not the best solutions for this xD.