Loc: Columbia River Gorge, US
Rodeos and fairs usually know how to do this, and provide adequate onboard generators. Bring power conditioners, and run laptops (if any) off batteries.
I've done this. Last time was about six years ago on a float sponsored by a club we were playing. Smiling and pretending you're having a good time is as important as playing - and it can be difficult as you're hanging onto your equipment for dear life. Floats tend to lurch around - especially when they make an unplanned stop. And that happens all the time on a parade route.
Loc: St. Louis, MO
Ed, I was supposed to play the Cottleville St. pat's parade on a float March 11. With the 30 deg temps and for casts of snow, they backed out, and I have to say I'm a bit relieved they did. Believe it or not, I've played on floats before....dating back to my college days in Rolla at St. Pats (hmmm, now that I'm typing this, a theme seems to be developing).
Just make sure you have a stable stand, they have an adequate generator, and don't forget to bring your UPS.
As for the bumps, I've had worse on stationary stages with a lot of bounce.
Acoustic/Electric stringed instruments ranging from 4 to 230 strings, hammered, picked, fingered, slapped, and plucked. Analog and Digital Electronic instruments, reeds, and throat/mouth.
My first adventure playing on a float - actually a trailer behind a truck with a loud intermittently working gas generator - was in 1970 for the Dory Days Parade in Pacific City, Oregon. This was when I first started playing keys in a band and my parents let me take out our Wurlitzer home organ. The band was promoting a concert later that evening at a popular teen dance club in a quonset hut called The Dunes by the Sea. Our drummer forgot his cymbals and had to drive back to Salem to get them. Our singer filled in on drums as we played the solo section of "Light My Fire" over and over minus cymbals. Then as we circled back to town on a curvy road through a forested area we narrowly missed and witnessed a head on collision. One car flew through the air and landed upside down in a ravine and a lady was killed in the other. The Dory Days Parade continues to this day but the Dunes is long gone.
In the early 2000"s I did several Q104 Cruise Around Manhattan gigs hosted by DJ Maria Molito. The band got lots of free advertising on the station. A fun gig but takes a while to get your sea legs on a rocking boat.
Then there was the Princeton University Homecoming where we represented the Class of 69 cruising around the campus on the back of a flatbed truck playing Woodstock era music.
Loc: Victoria, BC Canada
I did a parade when I was 16 - ragtime piano on an ancient upright. On the way back to the we hit a pothole and I hit my head on the piano when the old stool spun me around. I guess no concussion 'cause I can still recall coming to.
Loc: Northern California
Here's a link to a fun video taken from a flatbed truck on which the band Moonalice is rolling and playing in the Mill Valley CA Memorial Day Parade last year. Nice view of the band, the folks lining the road, and many interesting sites and Marin County characters along the way. It's a trip in both senses of the word. http://www.moonalice.com/tour/2016-05-30/mill-valley-memorial-day-parade
I did this two different years in college, both were solo gigs with just me (music-wise) playing my keyboard on our fraternity's float for the homecoming parade. We were on a flatbed pulled by a semi, and used a gas-powered generator, creatively hidden by other float decorations.
One year was a western theme, we built a saloon and a shell for my keyboard to look like an old upright to play ragtime music. The other year was an island theme and the shell was made to look like steel drums, so I played steel drum music.
I was in college, so I'm guessing I felt bulletproof and didn't worry any about risks to my gear. I don't recall having any issues either year.
Hammond SK1-73; Roland XP-80, JV-90, JV-1080, JV-1010, AX-1; Korg microSAMPLER; Boss DR-880; Beat Buddy; Neo Instruments Ventilator; TC Electronic ND-1 Nova Delay
Been there and done that. With a loud gas generator near by, crowds shouting (for the parade, not for us specifically), and limited space on the float for adequate monitoring (and all PA stuff pointing out and away), it was pretty impossible for me to hear what I was playing/singing. So, a sub-optimal set-up for sound (and, at least in my situation, we didn't really have much/any time to set-up in advance and do some real-world sound checking. And once the parade was going, all you could do was play).
Make sure you don't have speakers mounted up on poles (or on anything) without the whole thing being secured to the rig somehow. Also make sure that you have every piece of your set-up in sight and within reach at all times, in case you have to steady/catch anything.
That isn't as bad as it could be. I live in Minnesota in a town with REALLY bad paved roads (there is no excuse for this). My church had a Bluegrass Festival float in the Fourth of July parade about some years ago. It was basically an old hay wagon with a lot of hay bales and an amp or two (for vocals?). They had an entire 7-piece(?) bluegrass band up there performing for two hours in 86°F humid weather. Keep in mind, everyone basically sat on hay bales and tried to stay steady while they played as the truck went around turns, etc.. The trailer had hay bales all around the outside perimeter as well and most of the band was up against the vertical back panel, so I suppose that helped. I was only one of the people who hands out flyers and freezes, so I got to watch everything that happened.
As I mentioned, the roads here are terrible, even though my town supposedly has one of the largest Fourth of July celebrations in the entire Midwest. Potholes everywhere some years, and this last year a section of one of the main streets was starting to cave in right before the parade.
Anyway, I agree with the poster who said to fasten everything down.