Take a deep breath, hold it in for 15 seconds, now blow through pursed lips onto your hand from about a foot away. The air coming out of your lungs is a couple degrees warmer than the surrounding air, but it still feels cold.
This is because the stream of air mixes with the surrounding, cooler air, rips away the ultra-thin film of warm air around your skin, thus exposing it to colder air and creating a more efficient heat-exchange with the colder air, cooling the skin.
Even if your ceiling fan moves air an entire degree warmer towards her, the movement of the air still strips away the protective film of warm air around her skin.
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