Final answer:
Physical geography, particularly the freezing of the St. Lawrence River, critically influenced British strategy by isolating Quebec and forcing defenses with limited resources. The Americans attempted to capitalize on this but were hampered by the harsh winter and time constraints before British reinforcements could arrive.
Step-by-step explanation:
The physical geography of North America played a crucial role in shaping British military strategy during the attempts to reach and fortify Quebec. The freezing of the St. Lawrence River, a key waterway for transport and supply movement, created an isolated situation for the British forces stationed in Quebec. General Sir Guy Carleton, aware of the frozen river and the impossibility of receiving reinforcements, had no choice but to strengthen Quebec's defenses with the troops he had. Moreover, British successes in previous conflicts like the capture of Fort Louisbourg highlighted the importance of the North American theatre and the strategic value of controlling the waterways, as it hampered French abilities to resupply their forces downstream.
The attempted alliance with the French Canadians by Colonel Benedict Arnold, who planned to capture Quebec, was also influenced by the physical geography. Arnold perceived the isolated and resoundingly French Canadian population of Quebec as potential allies against the British. Unfortunately for Arnold and his force, the unyielding climate, with its winter freeze and limited timeframe before British reinforcements could arrive in spring, made their situation dire and ultimately led to their failure to take Quebec.