Is there a problem installing a floodlight upsidedown?
There isn't a problem mounting those Chinese jobs upside down -- per se.   For LEDs, orientation is not a big issue; it helps if the heat sink (if any) can have good convection but that can happen in several orientations. 

Of course that depends on their build quality, which can vary dramatically amongst brands/makes in that general category.  In that case, shelter makes more of a difference than orientation.   I am rather fond of mounting LED lights of that type inside the diffuser of old 100-175W discharge lights, where you can barely tell they're not a discharge light.