I agree that there should be a way, and in fact, they're required on nearly all construction/industrial sites on all vehicles. I've seen (heard) plenty backhoes with HST that certainly had them.
Do you have HST or manual transmission? The HST might be the easiest to mount a switch on, but keeping it adjusted so that it only beeps when you're actually backing up, but doesn't when you take your foot off, the treadle will be the challenge. A mercury switch sounds like a good idea, but any incline at all is going to affect how well that works. The actuator for the switch would need to be partially loaded on the neutral position, but obviously, you wouldn't want it caterwauling at you while you were sitting still. I don't know if there's any external line to permit using a hydraulic pressure switch to detect reverse motion.
As annoying as backup horns are, sure beats the hell out of being sued because you didn't warn someone that you were backing up. I have one on my F-150 LWB Crew Cab with a contractor's cap on the bed because it has a lot of blind spots and I want everyone around me to know that its going backward. It's big, it's red, and it goes "BEEP-BEEP", so claiming they didn't see me or hear me ain't gonna hold water.
I don't do any snow plowing. In Alabama, 4 visible snowflakes shuts the state down. I kinda like it that way.