I am in O'Fallon, Missouri and today it is -15 °C (5 °F) outside. I was taught water freezes at 0 °C (32 °F). I could understand if it was exactly 0 °C (32 °F) that the water might not be turning to ice, but how can it be 15 °C (27 °F) below water's freezing point and still be liquid water? The water is still moving due to the wind, which I think shows it has no plan of freezing. How can this be? 

My question may be too broad because there may be more than one reason why it isn't freezing, but I don't know of any. I tried to narrow it by giving my exact location and temperatures. It is a pond in my backyard. From what I've seen through Google, it may have something to do with crystallization rate? Thanks in advance.

Water melts at 0 °C (32 °F) but freezing is a more complicated affair.  It is  safe to say water gains the ability to freeze at 0 °C, but it can get much cooler before it actually does so resulting in supercooled water.  Water in this state can rapidly solidify when suitable ice nuclei are introduced.  For example, in convective clouds, liquid water can be observed at temperatures as low as -40 °C.  However, the water in your pond isn't supercooled.

You say the air is 5 °F, but what is the temperature of the water (probably above 0 °C)?  Ultimately it is the water that needs to be below freezing for ice formation to occur. How deep is the pond in your backyard? Water, compared to air, has a much better ability to retain heat and the bigger the volume of water, the more of a heat reservoir you have to deal with.  Freezing itself is an exothermic process and ice formation will heat the surrounding water.  The pond is probably not pure water and full of ions (e.g. salts) it has picked up from the ground, which lowers the melting point of water. All of these effects make it more difficult for water in your pond  to actually freeze and could explain what you are seeing.

Of these effects, the heat capacity of the water and the temperature of the ground underlying the pond are probably the primary contributors. Underneath the pond is the ground and it too is a heat reservoir. Both are probably warmer than the melting point of water even though the air temperature is much colder.  If a fluid is cooled from above, the cool fluid sinks toward the bottom.  If a fluid is warmed from below, the warm fluid rises.  Only one of these needs to be happening to start convection but it is likely that the ground below the pond is warmer than the pond and both the warm ground and cool air will drive convection in the pond.  This, in turn, means your pond is well mixed and you will need to extract enough energy from the system to cool down all of the water and cool the ground below the pond to give ice the chance to form on the surface. This will take time (on the order of days/weeks) of continual sub-freezing air temperatures to accomplish.  You'll have a much easier time freezing your pond than a large lake, but it still won't be an overnight process.
