The first and most important point to remember, is that you have to carry and cook all your food.
Avoid carrying water. Take powdered milk (not fresh milk), dehydrated meals rather than fresh meat & vegetables, dried fruit rather fresh fruit etc. Don't take whole packets - in many cases you can weigh out just enough for the trip plus a little extra for delays or emergency.
Avoid carrying tins of anything. Tins usually have quite a lot of liquid and you will have to carry a tin opener plus carry the empty tin back out.
Don't rely on the hut having gas cookers or that there will be a good wood stove or fireplace. Take you own small gas cooker with enough gas for the trip.