Ten coats in Wolf Customization are locked initially and cannot be applied to the player's wolf. These coats are unlocked when the player raises a pup with one of these coats to late summer (the start of the Growing Pups quest). At that point, the pup will have that coat in-game, and in the Family Tree, and the coat will be unlocked in Wolf Customization panel.
Unlockable coats are saved to your WolfQuest game account, so as long as you have created an account, they will be unlocked if you later switch to another computer or device.