We could, but it's far easier to transport large quantities of water than the much smaller quantities of liquid nitrogen that we could make.

You are correct! Fires can be put out with liquid nitrogen. It works because the liquid nitrogen deprives the fire of oxygen- thus smothering it. There is nothing special about a forest fire (except for its size), so scientifically, it can be put out with liquid nitrogen just like any other fire.

However, practically speaking, the size is a big factor, and producing/distributing the amount of liquid nitrogen needed to control a forest fire would not be very feasible.

Here's the answer that makes sense to me: May 28, 2006 - “You can imagine how much it would cost to supply a similar amount of liquid nitrogen. It would cost billions of dollars to put out a fire.” article.

This link says you couldn't transport enough liquid nitrogen to the fire: here.

Here's the answer to a somewhat different question:
Turns out liquid nitrogen is no good for putting out burning oil. The nitrogen instantly expands 700X as it turns to gas, this throws the oil up into the air where it burns rapidly. Similar to how water reacts, just far more violent. Dec 25, 2015, watch here.

Let me share with you the following link, it mentions the only useful thing about liquid nitrogen and forest fires. I am a responder in Quora, so I can recommend it.
here.

Fires need oxygen and fuel to continue burning. You can use liquid nitrogen to put out fires because when the liquid nitrogen turns to vapor, it will suffocate the fire of oxygen, i.e., there will be so much nitrogen near the flames that there won't be enough oxygen to continue the burn. Your question is whether this effect can be used to extinguish larger fires like forest fires. The answer is "yes," but you would need so much liquid nitrogen. The real challenge is not in the science of extinguishing the fire, but rather in the engineering.

What equipment do we need to store so much liquid nitrogen? How do we keep so much liquid nitrogen cold enough by the time we deliver them to the fires? How do we discharge the liquid nitrogen effectively to cover such a large area? Also, can we solve these engineering questions with technology that is affordable? If we develop the best liquid nitrogen fire extinguisher system, but it is too expensive, then no one would pay for it, and in the end, no one would use our technology.

Theoretically, wildfires could be put out with liquid nitrogen. In order to continue burning, fires require fuel, heat, and oxygen. When we put out a fire with water, we are really trying to absorb the heat with water so that there is no longer enough of it to keep the fire going. Trying to put out a fire with liquid nitrogen though is getting at a different aspect of the necessary items for a fire. With liquid nitrogen, you would be really displacing the oxygen around the fire, effectively suffocating it by taking away one of its main ingredients. The problem with trying to put out a fire with liquid nitrogen is how much more difficult it is to store and obtain than water.

When firefighters tackle forest fires, they are pumping water from somewhere to put out the fire. That water travels from the source, through the hose, and onto the fire. There aren't natural sources of liquid nitrogen that could be used for this purpose on the ground so that makes it difficult for firefighters to use. In addition, it could be dangerous because, like fires, humans need oxygen to survive. If firefighters are spraying liquid nitrogen around, they risk reducing the amount of oxygen around them to the point of making the air less breathable. There's a possibility that airplanes could also drop the liquid nitrogen, but that would still pose some difficulties with transporting large amounts of very cold liquid nitrogen.