The Silverthorn Antlers can be found on the first floor of the Clothing Store and purchased for 50 Bucks. Purchasing this hat will allow you to wear this hat only in Adopt Me!, unless you buy this item from the Roblox Catalog.
The description of this item on the Roblox Catalog reads
"Silverthorn powder is prized for it's alchemical properties. However, acquisition often proves problematic for unwary adventurers. The substance is unique to the antlers of the Silverthorn Stag, a beast of uneven temperament located only in the remote reaches of the forest of Arden."