did u flush the radiator? change all the main relay and especially fan relay. are you 100% sure the thermostat is working good and is not stuck open? also check fan timer.

I think your problem is electrial unless u see smoke coming out of ur engine.
the fan should not come on after u turn the car off in this weather and the fan usually turn on only when it needs too, like in the summer. if you can not fix the problem then take it to a honda dealer they will fix the problem on a heart beat.