Here is the list of Seasonal and Temporary Traits.
Note that None means they're not assigned to a season. This means they only appear for events and certain special summons.
Spring:
Fizz
Songbird
Bunny Ears
Insect Wings KIJI ONLY
Butterfly Wings KIJI ONLY
Full Beard
Multitude Fins TALLY ONLY
Butterfly Fins TALLY ONLY
Summer:
Fizz
Songbird
Roots
Filigree
Frilled Ears KIJI ONLY
Finned Tail Fur KIJI ONLY
Angler Lure KIJI ONLY
Small Dorsal Fin KIJI ONLY
Large Dorsal Fin KIJI ONLY
Sail KIJI ONLY
Dog Ears TALLY ONLY
Eel Tail Fin TALLY ONLY
Antennae TALLY ONLY
Feathered Spine TALLY ONLY
Medium Back Fur TALLY ONLY
Long Back Fur TALLY ONLY
Fall:
Skeletal
Wil o Wisp Ears
Wispy Leg Fur
Wooly Mane
Wooly Tail Fur KIJI ONLY
Furred Tail Fin TALLY ONLY
Winter:
Frosted
Glazed
Elk Horns
Moose Horns
Mammoth Tusks
Wooly Leg Fur
Wooly Mane
Wooly Tail Fur KIJI ONLY
Furred Tail Fin TALLY ONLY
None:
Filter
Crested
Fairy Points
Stickers
Frill
Feather Frill
Feelers
Plated Spine
Spiked Cheeks KIJI ONLY
Fluffy Cheeks TALLY ONLY