Is it possible to buy bitcoins via an exchange directly into cold storage? I own a cold storage wallet. I want to buy bitcoins, directly into my offline wallet (in order to avoid extra transfer fees).

I understand i have to pay exchange fees. What I want to avoid is: buy bitcoins into wallet H (paying exchange fees), and then transferring to cold wallet C (paying transfer fees). I do not want or need wallet H (hot), so I want it out of the picture completely. I have not seen any exchange advertising bitcoin buying into cold storage, that is why I am asking

Are there any services supporting this kind of setup?
You can generate a wallet for cold storage offline easily. You can then ask the exchange to use a public address of that cold storage as the recipient for a transaction. You'd still pay the fee the exchange demands to process the transaction though. 

Standard practice is that all trades in the exchange are just bookkeeping and are not published to the blockchain at all. Simplifying things a bit: The exchange uses a single wallet to receive all bitcoin transactions for all users. Each user is credited that much in their account. Trading moves some of the balance from one user to another. Once you withdraw, you withdraw from the shared wallet to an address of your choosing. In most exchanges, you can't trade directly into your own wallet.