Glyph origin of 「凉」 and its relation with 「涼」 「涼」 and 「凉」 are thought to have different origins, and are different characters altogether. From 《洪武正韻牋》:

本有凉涼二字，从冫者寒凉之凉，从氵涼德涼踽之涼。

Both these characters can be used for the meaning cold, but that was not the original meaning of 「涼」. 「涼」 was originally a type of light wine, and this usage can be seen in historical texts. From 《周禮‧天官‧漿人》：

掌共王之六飲：水、漿、醴、涼、醫、酏。

I had some more difficulty finding the origin of 「凉」. Websites like 小學堂 and 漢語多功能字庫 did not have entries for it either. According to this blog post, 「凉」 was a place name.

「凉」字則是地名，即是漢代十三刺史部的凉州，在今日甘肅省及寧夏全境、青海東北部、新疆東南部及內蒙古阿拉善盟一帶。「凉」字从仌的原因，相信是因為當地天氣比較寒冷，所謂兩點水的仌，即冰之本字，寒凉之凉為引伸義。

But when searching for 「凉州」, sources in Traditional Chinese tend to render it as 「涼州」, which leads me to question the claim that 「凉」 was originally a place name.


What is the glyph origin of 「凉」?
How did 「涼」 gain overlapping meanings with 「凉」?
Do 「淒」 and 「凄」 share a similar relation to 「涼」 and 「凉」?
李学勤《字源》 says:

谷衍奎《汉字源流字典》 says:

According to them, 涼 was the standard form and 凉 was the vernacular form with the same meanings. The People's Republic of China prescribed that 凉 should be the standard form and 涼 should be the obsolete variation form (异体字).
In Taiwan, 涼 is still the standard form and 凉 is 异体字. See 重編國語辭典修訂本: 凉 涼
According to the same sources, 凄 has a similar story but is a little more complicated, because PRC prescribed that 凄 should be the standard form for both 淒 and 悽. This also did not happen in Taiwan (you can't even find 凄 in 重編國語辭典修訂本).