-ㄴ다는 거 wraps a whole statement up into something you can know. 알아주시면 좋겠다 — 'I would like you to be aware' — is a soft way of giving advice, used twice here for dressing warmly and for where everything starts. 알지만 concedes instead: I know I should sleep with the fan on, but. Compare -ㄴ 거 알다, which points at one specific past fact rather than a general truth.