What day is the winter dream thing supposed to happen? And how many different dreams are there?
And can I attend events with potential husbands?

The Winter Dream occurs on the last day of Winter, if you pass up going to the festival on that day and just go to bed. It's a completely random event; you get one of several dream sequences, and you have no control over which one you get or whom you attend it with. It's just a fun little cutscene; it has no effect on your game whatsoever, no one will have raised affection for you if you get a sequence with him or her in it, etc.

Can I attend other events with soon to be husbands? And how do I ask them if i can.
(Besides starry-night festival)

Assuming you're referring to Harvest Moon DS {Cute}, there's also the Fireworks Festival on Summer 24. To ask someone to a festival, you must have their heart rate at green or above, and talk to them the day before the event to invite them.

what time do I talk to them?

Any time. Whenever you talk to them the day before the event, if they're at a green heart, they will ask you if you want to go with them.

how do I get adamant?

Isn't there a horse race festival you can get that at?
If there isn't I think you can get it in the 13th level in the mines in harvest moon more friends or friends of mineral town.