How did New Jersey's geography and population influence the outcome of events in the Revolutionary War?

New Jersey's geography and population were definite factors that influenced the outcome of events in the Revolutionary War.
In late August, 1776, the Continental Army suffered immense casualties after the Brooklyn Battle. Washington ordered his soldiers to retreat to Fort Lee, but the men did not linger at the fort. Instead, Washington led his men on a retreat march across New Jersey. The group of exhausted soldiers rested for two days in Hackensack, where foraging parties were able to amass abundant supplies from the surrounding countryside. The food refreshed the weary soldiers, and the short reprieve allowed Washington to make important logistical decisions.
The New Jersey population in the countryside was not especially supportive of Washington's troops, as many were Loyalists. These supporters of the English monarchy viewed Washington's bedraggled soldiers with a sense of inevitability; they believed that the war would end soon, with the British and Hessians as the victors. Washington made the decision to press on, ordering his sickest soldiers to march northwest to Morristown. The rest of the army marched south towards Brunswick, Trenton, and Princeton to join up with other militia members there. The author reports that the roads going south were "intolerable" and that the men suffered on the long trek. 
By the time the retreating soldiers arrived in Brunswick on November 29, 1776, there were only 3,000 men in the ranks. Many had already deserted the revolutionary cause along the way. So, New Jersey's unforgiving terrain and its largely Loyalist population led to mass desertions from Washington's army. Meanwhile, British forces pursued the Continental Army across New Jersey, and the cities of Trenton and Princeton hosted the English in large numbers. In these towns, British soldiers arrested Whigs loyal to the rebels and appropriated their farms and properties for their own use. Additionally, there was a large Tory presence in Monmouth county willing to sacrifice life and limb for the English king. 
Although much of the population in New Jersey consisted of Loyalists, there were some surprising holdouts. Many African-American slaves fought in support of the patriots. Additionally, some Quakers rejected their community's neutral stance and took up arms alongside the rebels. Meanwhile, some merchants and manufacturers chose to supply both sides of the conflict with ammunition, arms, and provisions. 
Despite the challenges, Washington decided to take Trenton and Princeton. He knew that Trenton itself had no walls or fortifications, a weakness that he could exploit. So, under cover of night, Washington and his men set sail across the icy Delaware River to ambush the Hessians and English soldiers stationed in Trenton. The river was unforgiving; the men had to cut their way through flat cakes of whirling flow-ice. Despite the treacherous river terrain, Washington managed to cross the river with his army largely intact.
So, New Jersey's geography and population greatly influenced how Washington fought the Revolutionary War. It is true that icy rivers, bad country roads, cold weather, and Loyalists made things more difficult for Washington and his men. However, the general was able to use these challenges to his advantage. For example, his bold decision to cross the icy Delaware River gave him the element of surprise he needed. Neither the British nor the Hessians expected such a maneuver in the thick of winter. Also, Washington found some surprising allies within the New Jersey population: African-American slaves, Quakers, and sympathetic businessmen who supplied the Continental Army with provisions, arms, and ammunition.