The traits I am referring to are characteristics that most clan born cats will have. The ones I am covering in this guide will be physical traits. A few examples of physical traits in main clans are:
RiverClan- Gray/Blue fur, Thick water-proof fur, Large webbed toes, Thick tail, Slender body
WindClan- Long legs, Pale Gray/Brown fur, Agile body, Short fur
ShadowClan- Soft underpaws, Sharp claws, Dark Gray/Ginger fur, Broad head and shoulders
ThunderClan- Gray/Brown/Ginger (most likely tabby) fur, Thick fur, Strong hind paws
SkyClan- Thick pads, Pale Gray/Ginger fur, Lean bodies, Flexible spine, Rudder-like tail
All of these are realistic traits that allow these cats to live better in their territory. Without the water-proof fur, RiverClan cats would become waterlogged and sink. WindClan cats wouldn't be able to twist and turn as easily running if they didn't have the agile body. ShadowClan cats wouldn't be able to sneak so silently if they hadn't had the tufts of fur beneath their toes to cushion sounds. The list goes on. All of these are very subtle things, though without them, the Clans would have died off quickly.
Now, when making a fan-clan, there are many things you have to consider before you come up with traits. Such as, Where do the cats live? What do they hunt? What is the weather like? What is the temperature like? Little things like the amount of undergrowth are important. If there is a lot of undergrowth, a cat would need thicker fur to avoid being scratched by twigs and brambles, though if a cat has too thick of fur, it will become snagged and tangled, thus making it a bit pointless.
Because of things like this, sometimes you have to consider what is more important to a cat's survival. Such as, would a cat be better off being able to hunt easily or being able to stay warm? Sometimes you will just have to compromise and choose something in between. For the most part, hunger comes after warmth, though there are a few special cases where that rule doesn't apply.
Some important things to think of, is first, is this really needed? You may want to have super awesome cats with thick rudder tails and enlarged arm skin flap things to they can leap from tree to tree, though if your clan doesn't live off of birds or fight that way, the cats would have never adapted that in the first place. Second is, will this hurt them in some other way? Almost always the answer is yes, though if the pros outweigh the cons, it is likely to stick. Take RiverClan's fat paws for example. They are perfect for swimming and catching fish, though reaching into a mouse hole or snagging woodpecker eggs would be a no-go
Lastly, think of if you've actually seen a cat with something similar or the same as the trait that you want in your fan-clan. Pay attention to that street cat that goes by your house or the kitty curled up onto your lap, they are both really good sources of information. If you can't do any of those, the internet is always a good place to look up cats.
Big cats tend to be a good bases as well. House cats are, after all, just teeny versions of the big ones. The best way to go about this way is to look up a big cat that lives in a certain region or biome that is similar to or the same as your clan. Lets go with snow.

Even though this isn't a big cat the lynx is a good point of reference. Lets state the obvious about this fella
He has big feet, a very large head for a cat, along with a short muzzle and itty bitty ears. All of these things help him in the snow. On a cat, these would be much more subtle, though there.
This guy or gal has all the same features, though they aren't as glaring as obvious. Plus look at that cutie i just wanna squeeze those cheeks