"明天不比今天冷。" 是一个不规范的句子。 “明天没（有）今天冷。” 是一个规范的句子。 ---------------------------------------- （不比）动词 1 比不上；不如 我不比你，文化基础太差。 2 不同于 今年不比往年北方不比南方，雨少，春旱严重。 以上来源于《现代汉语规范词典》

AS a native chinese,l think these sentences are the same.不如 can take the place of 没有 in this condition.These sentences both mean today is colder than tomorrow.

agree to Lingqun's answer. answer from 栗子 is wrong.

The first one means tomorrow is not colder than today (could be the same). The second one means today is colder. 明天不比今天冷 is grammarly correct. However I found it is little harder to understand. I would prefer to use the second one if possible.