(n.) a hard, keen frost
To dirl is to tingle or ache dully, either pleasantly or unpleasantly. A dirler, meanwhile, is an especially keen frost.
In etymological (and for that matter, meteorological) terms, dirler is just a figurative extensive of the earlier verb: the frost on an especially cold day could be said to have dirled the ground, the trees or the air, or you might feel a dull dirling or tingling feeling in your hands or bare skin when stepping outside.
Dirl itself is an old dialect word, recorded in the local Scots and North Country vocabularies since the 1500s. Among its many other meanings and uses, it can also be used to mean ‘to pierce’, and presumably the use of the word to mean a tingling sensation—like that of knocking your funny-bone, or experiencing a thrill of excitement—is a later extension of that.
That older meaning also points us in a plausible etymological direction too. The verb thrill originally meant ‘to pierce a hole’ (so your nostrils are literally your ‘nose-thrills’), and it’s likely dirl is just a morphed or somehow corrupted form of that.