Turn them off.
“Dripping” them would either result in ice building up in the hydrant pipe above the frost line, or
You’d be constantly dripping water into the ground, through the hydrants drain hole. This will just saturate your drain and use unnecessary water (pump, etc..)
Hydrants are an on/off mechanism. Handle “down” plugs the water supply and clears a drain path for the water in the hydrant pipe above the buried valve. This is so there’s no water in the hydrant above the frost line to freeze. Handle “up” unplugs the water supply and block the drain path so water goes up the pipe to faucet.
Opening the handle partially might just let water go to the valve’s drain hole once the path out the faucet freezes up, or because it’s less gravity to overcome.