If the airbag(s) deployed, there's usually significant enough damage to the front end that access to the engine compartment may be obstructed, so cutting the cables is usually required and we'll tape off the ends to make sure they don't accidentally make a connection. If taping isn't possible then we'll double cut and take a piece out of one of the cables.
On the other hand, if it's a mild fender bender and we want to just safe up the scene, we'll disconnect the cables at the battery and remove them from the posts, taping them as well to prevent accidental contact. The point here being that we want to minimize the damage to the car as much as possible, in a "customer service" kind of way.
The above being said, we'll only cut the minimum necessary to make the vehicle safe so usually we leave essentially all of the wiring in the car. But hey, that's just how we do it.
Most of the time it's just as easy to disconnect the cables in case you need to power up an electric seat or roll down electric windows later in the incident.
It's easy to tape up the terminals - it takes about 10 seconds - time well spent.
If you're going to cut the cables, roll down the power windows and move the electric seats as far back as possible before cutting the cables.
I would say double cutting would be right. We had a car fire one time and either single cut or disconnected the cables. After we got back to the station we got another car fire up the street from where the other fire had been.
You guessed it, the driver reconnected the cables and drove the car home and it caught fire again in front of his house.