It is possible. But you won't have a lot of time. It should take a minimum of 30 minutes, and easily an hour or more, to make the long walk from your arrival to immigration and then endure the sometimes long lines at passport control. Similarly, you should allow about an hour before departure (or start 20-30 minutes before boarding) to get through the baggage x-ray, then immigration, then security, then the long walk in the other direction to the departures area.

So you are pretty much restricted to meeting your friend in the airport. There is a food court on the mezzanine above the check-in areas (this is in the old terminal, I am not sure about the new T3). There isn't even a restaurant or cafe within a couple-minute drive from the airport -- Le Meridien hotel is an option, but with Dubai traffic and strange road patterns (i.e., having to drive a long way out of your way to make a U-Turn to get in), there is no way that you can get in and out fast enough to make it worthwhile.

I am assuming that you have a passport that allows visa on arrival. This is the case for European, U.S., Australia/NZ, and GCC countries, among others, and there is no cost.