While there is now a updated version of the Precipitation Map in the Texas A&M Meteorology Weather Center, this older map will give you an idea on how to use it. This map format is designed for forecasting precipitation type as well as precipitation amounts. Below is the forecast for the morning of November 14, 1997.
The green shading represents the precipitation amount over the preceding twelve hours. When skinny red contours are present, that means that the forecasted precipitation is convective. The winds are surface winds; the purple contours you didn't notice are surface temperatures.
The keys to forecasting precipitation type are the red and white lines. The solid red line is the 0C isotherm (freezing) at the surface; the red and white line is the 0C isotherm at 850 mb, about one mile above sea level. Although only single contours are plotted, it's usually possible to tell which side of the contour is below 0C by remembering that the temperature will generally be above 0C at the surface and 850 mb along the southern boundary of the map.
Where the air is below 0C at 850 mb and at the surface, it is unlikely that the air will be much above 0C at any other level, and the forecast will be for snow. An example of this would be South Dakota, where all of that precipitation ought to be snow. Here's the 12Z observation from Pierre, South Dakota:
KPIR 141151Z 35014KT 1/2SM -SN BR BLSN BKN015 BKN021 OVC025 M03/M04 A2980 R MK VIS1/4V3/4 SLP113 60001 70010 4/001 T10301040 11028 21032 52029=
On the other hand, where the air is above 0C at 850 mb and at the surface, it is likely that the falling snow will melt and the precipitation type will therefore be rain. An example would be South Carolina, where all of that precipitation ought to be rain. Here's the 08Z observation from Charleston, South Carolina:
KCHS 140756Z 36003KT 3SM RA BR OVC002 10/09 A2957 RMK AO2 RAB20 SLP011 P0009 T01000094 $=
Complications arise when one level is above 0C and the other is below 0C. In that case, the forecast depends on the details.
Suppose the 850 mb temperature is below 0C, and the surface temperature is warmer than 0C. You can presume that the precipitation will reach the 850 mb level as snow, and then fall into air warmer than 0C. Whether it makes it all the way to the ground as snow depends on whether the air above 0C is warm enough or deep enough. An example would be Oklahoma: perhaps in northern Oklahoma the surface air is barely above freezing and the precipitation would be snow, while in southern Oklahoma the surface air is well above freezing and the precipitation would be rain. Tulsa turned out to be rain:
KTUL 140553Z 31005KT 9SM -RA BKN020 OVC027 04/04 A2976 RMK AO2 RAB0456 SLP079 P0002 60004 T00440039 10044 20044 400610033 51019=
Now suppose the 850 mb temperature is above 0C, while the ground is below 0C. Now it's the sort of situation conducive to sleet and freezing rain. Which one develops depends on how deep the below-freezing air is near the ground. An example of this sort of situation is in southern Pennsylvania. In this case, Johnstown and most of southern and central Pennsylvania experienced freezing rain:
KJST 141147Z VRB03KT 3SM -FZRA BR BKN007 OVC010 M01/M02 A2956=