i don’t really see the point
of those “mostly like a flatwater k1 but maybe a bit more stable” boats like the burn and the jet. they’re not really rough water capable- sure they’re a little better than a serious k1 in chop, but only in the “surviving” sense, not in the “playing” sense. you won’t want to seek out rough water in one of those boats, no way. they seem to me mostly trainer boats for people who really want to paddle a flatwater k1, but haven’t developed the balance yet. i wouldn’t take one of those out on long island sound or the ocean in cold weather, that’s for certain.
you can paddle a ski just fine in cold weather- get a drysuit and some pogies and you are good to go. we paddle them here in MN until the water gets too hard to paddle, and we’re back on them after ice out. i’ve paddled xmas and new year’s day in long island (amagansett), with ice on the boat. i wouldn’t stay out all day, but a couple of hours won’t kill you.
Or get a fast rough water capable boat, like an Epic or an EFT. Those will make rough water fun, instead of a pain.