Do you have to wear a hat or anything? That would be my worst nightmare about an event like this!! Well, that and wearing heels.
No, you don't have to wear a hat and definitely don't wear heels. there is a lot of walking just to get there, and then you are on a lawn for all the time you are there.
The original dress you link to looks too short (though you might not be anywhere near as tall as the model). I think you would be far to hot in black tights and a black cardigan. There is very little shade, and, weirdly it is really unusual for them to have a wet or cold day.
The one @MamaDollyorJesus has offered you is lovely, and, if I can say so, the one @TheStirrer has offered is even better.
Both much more suitable than the one you linked to in your OP, and you wouldn't be worrying about putting your legs into Wintery black tights. 
It is a super day. I hope you find something and have a lovely time.