The term dad has origins in children's speech:
recorded from c.1500, but probably much older, from child's speech, nearly universal and probably prehistoric (cf. Welsh tad, Ir. daid, Czech, L., Gk. tata, Lith. tete, Skt. tatah all of the same meaning)
Daddy is the diminutive of this:
c.1500, colloquial dim. of dad, with -y
The OED quoted here adds more, saying:
Occurs from the 16th c. (or possibly 15th c.), in representations of rustic, humble, or childish speech, in which it may of course have been in use much earlier, though it is not given in the Promptorium or Catholicon, where words of this class occur.
Of the actual origin we have no evidence: but the forms dada, tata, meaning 'father', originating in infantile or childish speech, occur independently in many languages. It has been assumed that our word is taken from Welsh tad, mutated dad, but this is very doubtful; the Welsh is itself merely a word of the same class, which has displaced the original Celtic word for 'father' = Ir. athair.
A childish or familiar word for father: originally ranking with mam for mother, but now less typically childish. Cf. daddy.
?a1500 Chester Pl. (Shaks. Soc.) I. 43 Cayme. I will..Speake with my dadde and mam also..Mamme and dadd, reste you well! [Of uncertain date: the MS. is only of 1592. Harl. MS. of 1607 reads (ii. 678) 'sire and dam', (ii. 681) 'father and mother'.]
1553 Wilson Rhet. 31 Bryngyng forthe a faire child unto you..suche a one as shall call you dad with his swete lispyng wordes.
So dad or daddy stems from baby talk. This makes sense—f is a difficult sound for babies to say, but "harder" sounds like d are easier. Note, however, that just because many cultures share the same-sounding word (dada, tad, tata), this does not mean that one can make a clear distinction of origin. Though tata means dad, it does not provide substantial evidence that dad is from tata. As the OED points out, the form occurred independently in many languages.
I found one use of the phrase on a Prince fan site's discussion of the Beastie Boys. This is from an 8/16/11 post from user Cerebus (quoted in full in honor of MCA):
Been a diehard fan since License To Ill, which is like, 25 years ago. Been listening to the Beastie Boys almost as long as I've been listening to Prince. I love them. I love that they've changed over the years but are still clearly the Beastie Boys.
However, while I can still get way into all the older stuff (especially Check Yo Head and Ill Communication), I find it much more difficult to really love the last two albums. I dug what To The 5 Burroughs was about and I enjoyed that they took the beats back to an early electro hip-hop sound, but I still don't think its a great album. The new album, for as long as it took to get it done (regardless of the health issues), didn't really frost my pickle. Its good, and I can feel the magic trying to creep in, but again, not great.
I'll always be a fan and I'll always support them (including going to live shows if they ever tour again), but I think my real deep love for them probably ended with Hello Nasty.
So here it's being used in a positive way.
I found the annoyance sense of the phrase at a Yahoo Answers question from a woman divorcing her husband and looking to sell his baseball card collection. This is the top-voted answer:
well, hell, if's revenge you want why bother trying to sell them, give em away and tell him you did, that ought to frost his pickle!!
Could either of these posters be your mom?
Edit-- Keep finding more:
-One thing which frosted my pickle was no internet,and no
wireless.In 2011 this inexcusable
-I kept getting hassled by guys who thought they were smoooooooooooooth… their primary means of greeting females being to smack them on the butt. This really just frosted my pickle.
-I showed up for the meeting only to discover that it had been rescheduled. Now that really frosted my pickle!
I'd say the annoyance meaning wins out. Still no clue where it comes from, but it's definitely out there.
Edit #2:
After a little more looking around, I've found that the construction:
Well, don't that just frost your [fill in the blank]!
is a fairly common US colloquialism used to express annoyance or, more specifically, sympathy for someone being annoyed or vexed. In addition to pickles, the various things being frosted in these expressions include: flakes (after the cereal), balls (testicles), knuckles, feathers, asses, hides, and cakes.
I kept thinking this referred to frost as in damaged by cold, but this last one may hold a clue. These phrases could be a sarcastic reworking of the idiom
the frosting (icing) on the cake
by humorously emphasizing the unnecessary aspect of what has just happened. However, NOAD also has this informal definition of frost:
anger or annoy
such discrimination frosted her no end
So the question remains, is this informal use of frost a result of these colloquialisms or did frost carry this meaning before these colorful sayings were developed?
Best Answer
There's an article on the origin of "How's your father?" on the website of The Spectator, which references a listing it has been given in the Oxford English Dictionary. Both sources describe it as a nonsensical catchphrase traced to one music hall performer, Harry Tate. The OED even reports the phrase being used as a synonym for "nonsense" or "meaningless talk or ritual", as in "According to them, the Pope of Rome wore red socks when he was doing his 'how's your father?' stuff up on the High Altar."
The OED's third and final gloss for the phrase is "euphem. Sexual activity; sexual intercourse. Chiefly in a bit of how's your father." So, being an existing nonsense phrase, it presumably came to be used in sexual situations to substitute for more specific wording as to the behavior involved.