How can water exist in three states in freezing point?
If you only have a single component, water, present, then the liquid, vapor, and solid can only exist at the triple point.  If there is a second component present, say air, the phase rule tells us that there is an additional degree of freedom, pressure.  So, at a total pressure of 1 atm, the freezing point is 0 C (slightly lower than the triple point temperature), and you have liquid water, solid water, and, in the gas phase, water vapor mixed with air.