Although most people believe incoming SMS messages with AT&T should be free they are not. AT&T does charge per text message inbound or outbound. As should always be the case, read your contract with you cellular provider in detail to assure you will not have any surprises on your monthly bill.
If you have a plan for texting then you would not get charged for any incoming or outgoing SMS unless you go over the plan limits. If you have unlimited then you would never be charged anything additional. If you are asking if your incoming counts towards your limit of texting then yes it does.