Didn't we have some mules or something? I can't find any.
Anyway, we've got a horse, five carts, and six dwarves.
If I understand this correctly, each dwarf can carry a single barrel in their hands, as well as one in their backpack. Since each barrel holds 20 food/drink and it takes a week to get there and a week to get back (I think?), we're only netting 6 food and 6 alcohol per dwarf if they do 2 a day rations like we have been. Spending two weeks to buy us three days seems inefficient, if we can avoid it.
Carts, on the other hand, carry 360 food or drink, meaning 18 barrels. It's unclear what is needed to pull one.
Pack animals carry three barrels, so 60 food or drink, and need a bit of rope to lash them on.
With the animal and cart situation unclear, it's a bit hard to go from this point, but in general we should bring as many pack animals as possible (unless we're concerned about something happening to them in the forest, which is reasonable), and no more dwarves than are needed to pull carts.
Furthermore, it'd take 42 food/drink to last six dwarves a week (again, on rations as we are). Taking two barrels of food and drink each, and then some isolated food in pockets/belts, is probably ideal here. The only issue is that if there isn't any food at the camp for whatever reason, or if they're prevented from reaching it, they'll be SOL, so taking an extra four barrels might be worth it to ensure a safe trip home.
Assuming a dwarf can pull a cart on his own, we'd probably want to drop that to 5 dwarves, which means a little less than two full barrels of food and drink. Weapons may be carried on belts or slung across a full backpack, so no worries there.
I'd also be in favor of waiting a few days to mess with my treant and craft some goblets so everyone doesn't tantrum when we get back. I have no idea how much time we should take off before setting off again, however.