An adult bird will eat about 125+ grams of feed per day, so your two birds will eat about 2 kilos per week, somewhat less if free ranging. It sounds as if you have one of those Solway feeders with the optional rain hat, and if this is the medium size it will hold 2.5 kilos. If the birds were in a closed dry run with no access to other feed you would therefore need to refill the feeder once a week. In a suitably positioned feeder,whatever the type, the food will stay clean and dry, but leftover bits on the ground may go mouldy and then get picked up and eaten later on. A feeder won't appear to go down very fast if you feed them other stuff from the ground.
As these birds have just arrived with you it's likely that whatever you are feeding is new to them, and also they are still settling down together in a new environment, in difficult weather conditions, and thus are under a certain amount of unavoidable stress. Perhaps it would be best to try getting them into a routine of feeding from a feeder, on whatever you intend to maintain them on, possibly with a warm mash of some sort at the same time of day, every day through the winter, not just when it's a bit colder, so they come to know what to expect and benefit from the routine. That's why personally I prefer a quick and easy way of making this, as some days I wouldn't have the time to cook for them. As with livestock of any species, a certain amount of training into a new regime is needed and its good to try to avoid them getting into fussy feeding habits.