We're really lucky to have you as part of our community Rekoil, I love your creativity and giving spirit, and our forum is a more fun and caring place because of you.
I have contacted one of our administrators about a special badge to commemorate this winter event, and he told me that he would let me know soon. I have my fingers crossed, if there's any reason why they can't create one though we will still come up with something to reward members with.
The existing clubhouse badges are a couch for club members, and a little house for club owners. Moderators can award them in bronze, silver or gold with sparkles at our discretion, but admins I think can make the badge any color they want, which is why you sometimes see badges that are colors like pink or blue. So if they don't approve a new badge, they might be willing to bestow the existing clubhouse badges in a rare color like maybe something like red and green for the Christmas seasons, or an icy blue for winter, never hurts to ask.
If a brand new badge does get approved then you would pick an icon from this catalog.
https://fontawesome.com/v5.15/icons?d=gallery&p=2
While delibird isn't an option I'm afraid, there are real world birds, and a lot of winter holiday themed icons though like candy canes, gifts, sleighs, snowflakes, there's literally thousands of possibilities.
If you want a really specific design though we could maybe give out something like a trophy, like this one that members got during a clubhouse end of year festival last year. Fairy made this for the second place winner, which was a tie between the water Pokemon club and nature club. It's called the Silver Sylveon award. There's also a Golden Milotic for first place.
https://www.pokecommunity.com/showpost.php?p=10258465&postcount=47
Fairy is on leave right now, but we might be able to collaborate with the art studio or something to make us something. A special event like this one needs some extra magic.