I did H&V in September. The characters were dressed in Halloween costumes, stopped, waved, interacted with us, etc. The food was fall-themed with Halloween names ("Spooky Squash"). The Desserts were Halloween-themed with sugar eyeballs, bats, cats, pumpkins, etc. They played Halloween or Spooky songs (one of the few times I have heard Season of the Witch!). The characters just walk around and stop at tables. They interact with diners, pose for pictures, and then slowly make their merry way around the table. Minnie herself is at the front, taking pictures as her guests arrive.
There are links and reviews and I'm sure people have more pics, but I'm confident that the Holiday Dine is similar, but with Christmas theming.
It's a standard character dining experience. I don't know if you'll get a walk-up as Disney encourages use of ADRs. Check your app and there is likely an ADR available the evening you want.