If some particles of liquid in a solution convert to vapour then why can't some liquid particles convert to solid?
If water molecules go into the gas phase from the liquid then they are in a different phase. But water molecules go into the gas phase one at a time. If there are the same number of water molecules leaving the liquid as coming into it then the atmosphere above the liquid would have 100% humidity and be in equilibrium with the liquid. 

Now if some small number molecules of water happen to line up to form an ice crystal within the water itself what happens? Such an ice crystal is thermodynamically unstable and then "melts" within the liquid phase. Since the whole process takes place in the liquid phase it is virtually undetectable. 

Now you also have to realize that form ice crystals big enough to detect visually requires more than a handful of molecules. You'd need billions of billions of molecules. That is just a statistical impossibility.