Is it normal for actual temperature to be below target temperature during cold weather?
Your heating system is sized for your house and climate.  At some outside temperature, it will reach a point where ANY SYSTEM, running all the time, cannot input enough heat to compensate for the heat exiting via the roof, walls and windows.
The rate of heat flow equation  is analogous to Ohms law  I = V/R   Take I a rate of heat loss, V as the Temperature difference on either side of the wall and R as the Thermal Resistance of the wall.  The greater the temperature difference, the faster you lose heat.  When you lose heat, the rate slows down and you reach an equilibrium.

A heating system able to maintain 65 degrees in the coldest weather you experience is probably adequate, but barely so.  

Keep in mind that the ground itself also gets cold.  In prolonged cold snaps, such as we've had this winter, it is not surprising that you have a cold floor.  The ground might even have frozen underneath it.  This is not expected behaviour in Florida.

The fact that you're using heat pumps also comes into play.  We don't use them very much up here in Canada, because our winter temperatures are too low for them to work efficiently.  A heat pump is trying to suck the heat out of the outside air and dump it in the house (like a refrigerator running backwards).  The colder the outside temperature, the less efficient this is.