I have no idea with the seed, but after having grown it I can tell you the seeds would be very small, because the flowering parts are pretty tiny on these plants. I never had need of trying to collect seed because this can be grown so incredibly easily via stem cuttings. No clue on cold hardiness either, thank god, because I live in a place that typically doesn't get below 65ish F.
I might, however, be able to offer cuttings packed in baggies with soft moss to keep them moist. I send freshly harvested turmeric to my mom like that. I have to go back up to my place and check on the stand to see what would be available, so its not a for-sure thing as of yet. Let me know if that's of interest to you.