Possible Battle

The climactic battle was probably Guilford Court House, N.C. There were woods around the battlefield depicted in the movie. However, the large climactic battle wouldn't look so good on film if it was obscured by trees. It is true that Greene and the Americans withdrew from the battlefield, but they forced Cornwallis to abandon his Carlona Campaign and move to Yorktown because he had lost so many men. The battle was Hollywood-ized, Cornwallis didn't retreat, but Guilford Court House ended Cornwallis' domination of the South, and forced him to regroup at Yorktown, where he was cornered and thus surrendered. The 'climactic battle' depicted in the movie can thus be interpreted as a combination of Cowpens and Guilford Court House (which occurred occurred within 2 months of each other) into a symbolic decisive battle that forces Cornwallis to Yorktown, which the two battles did do.

It's Supposed to be Cowpens

It's supposed to be Cowpens because if you watch the credits, one of the characters is listed as Cowpens Soldier.

combination

I'd say the battle where Mel and his son watch from the farm house is Camden. We know this because General Gage (ah, this might not be his name) ran away from the battle, with his staff not far behind. I'd say the final battle is a combination between Guilford Courthouse (because Conrwallis did order his artillery to fire directly into British and American troops) and Cowpens because we held the field after that one.

The movie was never intended to be a factual retelling of the Revolution. It's a piece of fiction set during the period that takes great liberties with the facts, places, and people involved. Gibson's Martin character never really lived; he's a composite of several historical figures (most notably Francis Marion). The ruthless Colonel Tavington somewhat resembles the real-life General Banastre Tarleton, albeit very loosely, and likewise never existed in real life. It's reasonable to assume that the final battle is a very distorted and historically inaccurate interpretation of Cowpens or another battle, re-imagined in a way that would better fit the romantic and ultra-patriotic nature of the film, with many historical facts disgarded. The Patriot is not unlike Gladiator in it being a tale of fiction, with a fictional composite protagonist (Gladiator's Maximus bearing a resemblance to Cincinnatus and the real assassin of Commodus, Narcissus), being set in a real-life historical timeframe with real historical figures thrown in (Cornwallis in the former, the Emperor Commodus in the latter).