If I plug a two prong outdoor spotlight into a three prong grounded extension cord would water getting into the empty hole in the three prong cause the circuit to trip?
To answer your question, water getting into the ground terminal of your extension cord will not trip the GFCI. If water gets into that hole though, it will probably get into the hot or neutral slot and that will trip the GFCI. Get a light with a longer cord or use some of the power cords you see in stores at Christmas time (see below). most come with covers and although not meant for year round use, they usually are.
Strictly speaking, if everything else is wired and functioning properly:
The "hole" you're referring to is a ground, and it's exactly what it sounds like. That wire is connected to the ground. Water in that particular port will give you no issues. (though water across the other two blades will DEFINITELY cause issues! Your plug is not watertight - do not assume that your exposed socket is the only one vulnerable to water)
Extension cords are not meant to be ran through flowerbeds, etc. and should not be left outside for prolonged periods. Your landscape spotlight (If it is not a low voltage system) should be plugged directly into an outlet. I'd say your most advisable options are:
Replace the power cord on the light so that you no longer need an extension cord. This might take higher-than-average DIY knowledge to avoid setting your house on fire with the wrong sized wire run over too much length.
You could hire an electrician to install an outdoor outlet closer to your landscape feature. Definitely the safest option, and could add equity to your home. Gotta love landscape lighting at the flick of a switch.