What is the comparative form of холодный?
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-ей forms of comparatives are either colloquial or poetic, and in both cases they're used in free variation with -ее. A more formal style of speech requires -ее only.
Now as regards по-, there's a limited number of contexts where you'd use it. Firstly, when you talk about "a colder X" as opposed to "X is colder"; e.g. В странах похолоднее, вроде России или Канады, плотность населения меньше. "Colder countries such as Russia or Canada have lower population density." Note that you could also use поменьше in that sentence, which brings us to the second use of по-, which is a little harder to pinpoint. Say, in that last sentence, "a little harder" is a clear case for потруднее — which already kind of implies the "a little" part; but that doesn't quite mean that по- denotes a small difference; rather, that difference isn't great (so it could be small or just "regular"), but it's definitely one that you'd notice.
Another use of по- is to denote a desired increase in a certain quality. Готовят там отлично, а вот пиво могло бы быть похолоднее. "The cooking's great there, but the beer could be colder". Побольше бы таких сюрпризов. "I wish we had more surprises like that." (I know it's an adverb here rather than an adjective, but it works the same way.)