My guess is the issue is the contacts inside of the solenoid/contactor have some tarnish on them from the frequent on/off from plowing use. The switch on the handle bars is a low current momentary on, double pole switch that just closes the contacts in the solenoid.
@Foot0069, the relay in the picture you’ve attached would be much too light duty for a winch, although electrically it effectively does the same thing that a winch solenoid does. A winch solenoid is about the size of a pack of cigarettes (and only marginally more expensive).