You can ride in a car (most cars are enclosed vehicles with a door), but not a horse or bike. You ride on those. (IMHO you can use either on or in with a boat)
So #1 and #3 are wrong, though if you said this in spoken speech it's unlikely anyone would catch the mistake.
The clearest/right way to do what you're trying to do is this:
Police ride in cars, on boats, on horses, on bikes, or they walk.
The they before walk is not strictly needed but it helps to break up the "list pattern" established before and signal that you are introducing a new component of the sentence.
Ride without a preposition means enter a vehicle expecting that the vehicle will give you a ride.
I rode the trolley to the city's center
This means you got on the trolley, and took advantage of it's ride to the city center to take you there.
But I interpret #2 to mean use as a vehicle in a general sense, and I suspect most others would too.