There's certainly no significant swathes of arable land for several thousand feet below in elevation, and any beast worth hunting is likely also migrated to lower heights by this time of year. Given that it looks like they have no intention of moving they must have food stores prepared.
But there is a nearby stream which they likely use for water, though it is beginning to freeze over. You haven't seen anyone go there yet. But if you had to guess, similar to what would happen in a village without a well in the Riddermark, they likely make one trip a day with a group to get all the water they need for that day. And if such a fortress ever persisted through a winter in its past, the structure above at least must have a source too.
Eothain's plan is plausible, but it could result in a struggle and risks creating a commotion, and of course would undermine any pretense of a peaceful approach.
OOC:
Not saying the last part to dissuade you, just communicating the risks so you can compare it to your other options.
