The phrase hands down comes from horse racing, as explained by The Phrase Finder:
Jockeys need to keep a tight rein in order to encourage their horse to run. Anyone who is so far ahead that he can afford to slacken off and still win he can drop his hands and loosen the reins - hence winning 'hands down'.
And confirmed by Etymonline:
To win something hands down (1867) is from horse racing, from a jockey's gesture of letting the reins go loose in an easy victory.
I found this antedating of the phrase from The New Sporting Magazine, 1855:
And I found examples of the phrase being used figuratively in other contests by the early 1880s.
"I'm down with it" or more often "I'm down with that" is confirmation, acceptance as in "that's fine by me", or commitment. It's originally African American jazz slang from around 1935.
It was popular during the 1990s especially in rap and hip hop, also in the 1970s, and in jazz from the 1930s to at least the 1960s.
Definitions
Webster's New World American Idioms Handbook (2011) says:
I'm down with that: slang; means “I'm agreeable to that”
A poster on Wordreference.com (2006) said:
In AAVE [African American Vernacular English] "I'm down" or "I'm down with that" can mean "I am in", I will commit to that action or position, or I am on your side.
Our Souls to Keep: Black/White Relations in America (1999) by George Henderson equates "I agree" with black English "right on" and "I'm down with that".
Law Enforcement Vocabulary (1973) by Julian A. Martin:
I'm Down With You. Juvenile slang: I'll fight on your side.
This version was used in Buffy The Vampire Slayer in 1998, showing overlap between being friends with someone or generally agreeable with them, and and described as mainstream slang in the book Slayer Slang: A Buffy the Vampire Slayer Lexicon (2004) by Michael Adams (first published online in 1999):
If Faith's Goth-chick slang veers towards the obscure, other characters favor the teen mainstream: ... "So, you're not down with Angel," she acknowledges of Spike, Angel's rival among Sunnydale vampires; ...
The American Heritage Dictionary of Idioms (1997) shows a slightly different use:
4. be or get down with. Be close friends with, as in I'm down with that crowd. [Slang; late 1900s]
From the introduction to A Jazz Lexicon (1964) by Robert S. Gold:
A few terms, perhaps because of their simplicity and
widespread applicability, have survived from the early jazz
life... The jazz slang speaker's
aloofness is tacitly justified by his feeling that only those
who are down with the action (aware of what is going on)
should have access to the speech of those who have paid
their dues (suffered an apprenticeship in life generally and
in the jazz life in particular).
And its own entry (read online):
down with, [poss. from gambling slang to be down
(i.e., to have one's bet placed) and poss. from general
colloquial down to his toes (or socks); current esp.
among Negro jazzmen since c. 1935] See 1957 and
second 1959 quots. — 1944 Dan Burley's Original Handbook of Harlem Jive, p. 15. "I'm down with the action."
— p. 41. Othello, the spade stud, pops in port, "down
with it, cause he can't quit it." — p. 47. Iago is down with
the action. — 1946 Really the Blues, p. 369. down with it:
top-notch, superlative. — 1955 Down Beat, 5 Oct., p. 51.
I don't know who the singer is, 'cause I'm not down with
all the singers now. — 1957 The Book of Negro Folklore,
p. 483. down with it: to get acquainted with, to understand. — 1959 Diggeth Thou?, p. 23. Let's see what's
down with the deal. — 1959 Esquire, Nov., p. 70I. down
with something, to be: to know something thoroughly.
— 1960 Beat Jokes Bop Humor & Cool Cartoons, p. 57.
The Ham wasn't down with the action.
Early examples
From an interview with rapper Guru from Gang Starr in Blues & Soul magazine (1990):
"You see I'm down with anything that's about uplifting and giving self-esteem to the black man. You see the black man in cities in America, over here and around the world . . . they need self-esteem because a lot of them see it as society's so hard on them they can't get it together. What these religions are based on is building pride, awareness and knowledge of culture and self, and that is important. So, anything like that I'm down with. That's why I say 'I'm down with the Nation [of Islam]"
Ebony magazine (January 1976):
Buffalo's Randy Smith, a former NSSFNS recipient, said he was determined to make the tournament, with or without his club's blessings. "That's how most of the players felt," said Smith. "The tournament is designed to help black youngsters, and anytime there is something I can do to help the cause, hey, I'm down with it."
New Black voices: an anthology of contemporary Afro-American literature (1972):
"Don't bet on that. Chumps like to deal with a winner, if you know what I mean. I'ma stone hustler. I'm down with it, dig? And he threatened me, even if it was with ...
From Mezz Mezzrow's autobiography Really the Blues (1946) , in a reference to jazz slang of the 1930s:
first cat: Hey there Poppa Mezz, is you anywhere?
me: Man I'm down with it, stickin' like a honky.
A translation of terms appears in the glossary:
Down with it: top-notch, superlative
Best Answer
The association between primrose and pleasure comes from its status as an early spring flower, and that flower's association with maidens and pleasure. According to the Oxford English Dictionary, the word comes from Anglo-Norman primerose, lit. first rose. (Compare primerole, another word that referred to early spring flowers like the daisy, primrose, and cowslip.) The Middle English Dictionary entry gives lots of examples of early usage for primrose.
First, it helps to know that these flowers were eaten. Your question reminded me of a Middle English lyric, Maiden in the Mor, which uses the primerole as a food (mete) consumed by the eponymous maiden:
What? Eat flowers? There is a naturalistic edge to this (surviving only on flower), but primrose was also known as a pleasurable, sweet food! In a late medieval cookbook (BL Harley 279), mixing up flowers to eat was delicious (again from the Middle English Dictionary):
So we have flowers, eating, and maidens. Any eroticism is through association with spring and maidens, who are (a) pure and (b) ready for sex, marriage, and/or childbirth. Here is a stanza from the fifteenth century poem Ave Regina Celorum by John Lydgate, where the primrose is used to describe Mary:
Mary is the primrose of pleasure, the flos florum (flower of flowers). If there is any erotic sense here, it is subsumed under God and Mary's role as the divine maiden, mother, and wife. Still, the connection to pleasure is there, and it appears in other texts. For example, back to the Middle English Dictionary, there is this example from a fifteenth century lyric:
Plesaunce is a common collocation for primrose, perhaps because of the alliteration. So the primrose is a flower of pleasure, either in taste or in other figurative use.
In these and other examples, I find no reference to such pleasure being a negative thing. Given that absence (an an Early English Books Online search mainly revealed references to herbology or to people in positive senses) I suggest that any negativity would be context-dependent. So the notion of the primrose path as negative depends on its context in Shakespeare, not on any quality of the primrose.