About 30% of my foodplot is trail. Mow 4th of july, spray iand spread seed in august. Young rye, oats, clovers, even most brassicas survive mild ATV traffic. My tail is a public snowmobile trail. Technically ATVs other than my clubs hunting lease folks are not supposed to be on it. But, probably get double the traffic from illegal joyriding.
White clovers seed more than red ones, so when you mow the white clovers set a new set of seed heads that are probably fertile in a month. Red clovers are maybe 2 seed heads a year. You mow, it mgiht not put a new seed head out. Kale family and rape survive atv traffice better than turnips or radish does. Seen native chrocry survive ATV traffic on other trail systems, so that should be ok. Winter peas usually get devoured before they get mature on my foodplots up there.
I dod not plant platain on my foodplots, but they are in the driveways and club lawn areas. They survive traffic too. Small gme loves crabgrass, deer will eat it late summer / early fall.
Timothy survives ATV traffic ok, but deer arent a big fan of it.
I know a few people that only mow around labor day and deer enjoy the fresh fallow food it provides. Some years they lime, some years they run the discs stirring up things. MAybe every few years they buy a seed mix, but dont spray. OFten the deer enjoy grape and other browse along the trail.