We have a mail slot I've been meaning to address since we moved in, so no direct help here. BUT...
When putting something in a neighbor's slot it appeared they had some kind of pouch or sleeve on the inside of the door. I've been thinking a pouch could be nice because it could hold letters and prevent the mail being scattered around the entryway every day. But, it could be a problem for large/weird packages that come through the slot.
But, a basic fabric sleeve that's larger than the slot would be more flexible in terms of larger envelopes, etc. and it could simply 'flop' down to cover the slot and insulate it the rest of the time.
This is definitely not worth the amount of time I've devoted to thinking about it so far. =)