Hi there!
I have Khaki Campbells (is that what you are talking about when you say khaki ducks??).
I let them free range during the day, but bring them in a fenced in area at night to keep them safe. The have a coop in the fence so they can go in if they want to. Generally, they sleep outside. Their grain is in the coop, but since they forage during the day they don't usually eat much grain. I have a large kiddie pool in my yard and in the fenced in area for them. They don't usually swim, but they will get in there and clean themselves, then get out. I have to change it daily though, they are very messy! (that's why it is outside and NOT in the coop!)
They are too heavy to fly, so they don't usually go far. They will flutter around the yard though, it kind of looks like they are trying to fly!
As for winter, they LOVE the snow. Just like in the summer, they have a choice to go in or out of the coop. They generally stay out, even if it's snowing! I switch out the kiddie pools for rubber tubs, that way I can easily break the ice. You can also use a metal tub and put a water heater in it. I am debating trying that this year. Last year I had to water them 3 times a day (and break ice), but they are my pets so I was glad to do it
So to answer your question, no, they won't fly away for the winter. They can't really fly in the first place, and as long as you provide then adequate food, water, and shelter, they won't wander off
And the Khakis are WONDERFUL ducks to have. They are a bit more nervous than other breeds, but they can be very friendly if handled a lot when they are little. Mine are excellent layers. In fact, they out-lay my chickens! I get an egg a day from them even in the winter. I have a heat light in their coop for them, but since they don't go in there much I don't think that really matters.
I had mine with my chickens, but my drakes were mating with my hens
So I had to separate them, the hens weren't too fond of it!