how big are the FETs used to drive Tesla cars
They don't use MOSFETs at all- they'd be too expensive in such high voltage (375V battery voltage). They use IGBTs, in banks amounting to something like 66-72 total of them for all three phases, reportedly. 

The Tesla motor can (briefly) produce something like 400HP (300kW)- some of the data says 185kW which may be more sustainable- which implies currents in the 250-800A region. So maybe 60A/600V IGBTs, but I'm not sure anyone has publicly given the part number. 

Nice car by the way, a colleague has one.