Is it Ok to mount a bathroom extractor fan at floor level?
First off, you misunderstand the intention of the extractor fan.  It is not to remove hot air.  It is to remove moisture from the air, and that's done to help protect against mold and mildew buildup.  This is particularly important in bathrooms where the door is usually left shut.  

(It still helps with open door bathrooms too but in those cases the moisture will dissipate into the rest of the house on its own if a fan isn't used so it's less of a concern.)

Typically the moisture will be in the form of steam and will tend to want to rise to the ceiling.  In the "door shut" scenario the air will be coming in through the base of the door - so putting the fan on the floor won't really help remove any moisture.