The cool air you're feeling is mostly likely from the fan, which sounds like is mounted on the bottom of the unit. Refrigerators work in theory the same as air conditioning units. Freon circulates through the system, and as it attracts heat, this heat needs to be released to the "outside" of the unit. That's where the fan comes in. It pushes/pulls cooler air, typically across a condenser, which the heat transfers to and gets pushed out into the room. As a result, the refrigerant/freon passing through the condenser is now cooler/colder, so it travels back to the compressor, and eventually draws out more heat from inside the refrigerator. As more and more heat is extracted from inside, then the inside becomes/maintains it's colder temperature. IOW, it's operating as designed.
As far as safe, if you're willing to take a chance on it, then just thoroughly clean it out/sanitize it before storing food inside. Unless the previous owner was storing some kind of infectious/biological/toxic chemicals in it, you're probably fine. Of course, you should also plug it in and let it run for a day or so to ensure it keeps running before going to the trouble of putting it inside, as well as stocking it up with food/drink.
If it was free, then I wouldn't worry about the "economics" of how much energy/costs will be involved. That's kind of like looking a gifted horse in the mouth. If you needed a car, and someone gave you a free one that was not as economical as others, then would you turn it down? How much electricity could you pay for to run the frig. that would amount to the cost of a new one, as well as the cost of the assoc. electricity to operate it?