Snow is just ice crystals aloft that fall and never unfreeze because the temperature at different levels it falls through is always below freezing, this includes the surface being at or below freezing.
Rain starts as ice crystals aloft but when it falls into warmer air a loft that is above freezing it unfreezes and turns into rain. The rain never falls into temperatures below freezing again so it stays in liquid form until it reaches the surface.
Sleet starts as ice crystals aloft like snow, but then falls into warmer air that is above freezing and melts into rain. The liquid then falls into a deep cold pool, where temperatures are below freezing and refreeze into ice crystals before falling to the surface which is also at or below freezing. (Sleet is NOT hail. The difference is how they are made a loft)
Freezing rain, like sleet, starts as ice crystals aloft and falls into warm air and unfreezes. The difference between the two is that the freezing rain doesn't fall until a deep cold pool of air below freezing, so it does not get the chance to refreeze. So the liquid reaches the surface, which is at or below freezing, as rain and freezes on contact.
So we now know warm air a loft is important in forecasting between snow, sleet, and freezing rain but how do we determine what the temperatures up in the sky will be? For this we look at a thermodynamic diagram, which we call a skew-T or a sounding.
The sounding above is a freezing rain sounding. The blue line is the 0 degree Celsius line, everything to the left of it is below freezing and everything to the right is above freezing. The red line is the temperature line and the green is the dew point line. Start at the top of the graph and pretend you're an ice crystal and follow the red line down. You will see you are above freezing until about 800 mbs up in the atmosphere. Then the red line goes to the right of the freezing line which means the air temperature is above freezing and you would melt into liquid. As you continue following the red line you go back to the left of the freezing line but do not have a chance to refreeze before you hit the surface which is also below freezing so you hit the ground as rain but freeze on contact.
Hopefully this gives you a little insight on how we forecast for the different types of winter weather!