Having the Mediterranean Sea on one side has given Syria a Mediterranean climate with arid, extremely hot summers and moderate winters, with snowfall once in a while. As you move inwards from the borders, it gets drier and quite inhabitable. It's a dream to live on the coast lines with their mild temperatures in summer (July) and bearably cold winters (January).
As you go higher up towards the Anti-Lebanon Mountains, temperatures in Syria reduce with progressive altitudes so even summers are cool. On the other hand, the mountains receive snowfall in winter, making it extremely cold. The desert zones like Palmyra have the extremes of both summer and winter. Summer days are sweltering and winter nights are freezing. In fact, the Khamsin winds from the east sometimes accompany the end of summer and getting caught in them can be a brutal experience.
Rainfall along the coast lines and the mountains tend to be average to heavy, with precipitation ranging between 25 cm in the east to 125 cm in the mountains. The coast line receives average rainfall. However, Syria tends to experience dry years where rainfall is negligible. The rainy season in Syria is between November and April-May.
Frost is highly unlikely even in the mountains, though if you're lucky enough, you can spot the Jabal an Nusayriyah Mountains with snow-caps deep in winter. Temperatures in the mountains hit a maximum of 27° C whereas in the deserts, the highest recorded temperature in the middle of summer has been 43.3° C.
Spring months of March to May are the best time to visit Syria, when you can enjoy cool days and see Syria's flora in full bloom. However, if you want to avoid crowds, then autumn, in the months of September to November, is your best bet. Winters are best avoided, but if you want to see snow-capped mountains, pack some heavy woollens and go for it.