Snow and rain. There is no relationship between rain falling and snow falling; i.e. rain does not need to precede snow. Snow is created as a result of water vapor condensing into solid particles. Whether an area gets rain or snow is dependent on the temperature; snow forms and starts falling high in the atmosphere and will reach the ground as snow only if the ground temperature is zero or colder. If the ground temperature is higher than that, the area in question will get rain not snow.

As for the global warming clarification- Amman used to get snow in January many years ago. For example ten years ago, on January 13, 1998 Amman witnessed 30 cm of snow and in the south it was as high as 2 meters (http://www.jordanembassyus.org/Jan1398.htm). So the sight we woke up to today brought back childhood memories. This is how I remember Amman all my life, not snow in February and March, but also in January. Lovely.