The first quote wants a little more context, but all instances (including the three songs above) seem to describe a popular and innocent social pastime.

The doctor seems to be saying he finds his work so rewarding that even in the midst of pestilence he loves what he's doing. Helping people in need brings as much joy as a dance party or a country picnic.

The newsboys were being treated to a day in the country, something most of them had probably never experienced. It featured a dinner, country-style food, no doubt, presumably planned and catered for them. (Was "Unity" a church publication?) I'll bet the organisers deliberately borrowed the familiar "huckleberry picnic" phrase in the same nostalgic spirit that bills such a day trip today as a "country fair" complete with motorised "hayrides," or would advertise a catered dinner as a "potluck." (Yes, I've seen the latter word misused this way.)

In every example except Frank Dumont's pseudo-hymn (?) and Woodworth (1852) where the participants' ages are not implied, the huckleberry picnic seems to be a celebration associated with youth (or animals acting like kids):
* In Kickin' Mule it's a place to meet a girl.
* The quotes from 1865, 1875, and 1888 feature children there.
* It's hard to know without more context, but I'd conjecture the people addressed in the "Arthur's Home Magazine" quote were younger than the speaker.
* The doctor in 1885 couples it with another fun social pastime especially enjoyed by youths.

What were the "skippers" or "skeppers" on the meat? Greenflies attack people, not food. Dinner on the ground also implies an outdoor event with too many dishes to fit on the table, or else no table present, though they seem to have set up oven as well as cookfire at this picnic.