I would like to observe that not all extension cords are alike.
That is, it's one thing to run a large appliance using a 500-ft. cord made of #18 zip wire, and another to use a properly sized cord, of the appropriate type, and of minimum length.
Those do-gooder (usually government funded) flyers that get passed around are always making blanket claims; a common bit of art shows an extension cord with the international 'forbidden' traffic symbol over it.
Staying closer to the OP's concern, one must remember the inrush current for a motor is quite a bit higher than the running current, and that an undersized cord will have the effect of reducing the life of the appliance. There are also all the other issues associated with cords: loose plugs, damaged cords, etc. Just because there's no specific rule forbidding something, it does not follow that it's always a good idea.
Look at it this way: there is no code requirement that there even be a receptacle for a refrigerator, or that the fridge be in the kitchen. "Code minimum" guys will quite happily omit such a frivolous thing - leaving the occupant to take the hit from the 'extension cord police.' Something to consider.