I could see them doing a 10 mile march (not that far, honestly, even though it seems ridiculous to the modern sensibility) without shoes in winter. Their feet would be absolutely fucked once they arrived and probably would have lost some toes but it's doable certainly.
I used to walk 5 miles to work (obviously with shoes) every day and it didn't take me much more than an hour.
If the terrain didn't have too many obstacles to poke feet it wouldn't be the worst march ever.
What about the dozens upon dozens of miles they marched before they made their final trip to surprise the Hessians? Were they shoeless then, too?
I'm telling you, they'd all have lost their fucking feet. Army life is rough. Taking care of your feet is a goddamned art they taught in the US military. I'm not even joking, it's very serious. A soldier with a bad foot is a liability to all the soldiers with good feet more often than not, just like a bad shot is a liability to a rifle team. They'll get you fucking killed, man.
The men back then would know this, too. They don't want ol' clubfoot Kenny rushing in to bayonet drunken Hessians with them. They want Chad Thunderdick and his nice, polished boots and good diet and high motivation at their side. Washington would know this, he seemed to understand soldiers very well, knowing how to keep them motivated. I don't know if any other man could've kept the "continental Army" together for as long as he did, fleeing from the British for most of the war. Without a strong leader, men would desert in droves or become agents for the British and really fuck your shit up.
All because you couldn't provide them with fucking shoes, one of the most basic human necessities, especially for marching. Not even makeshift sandals? Wrapping your feet up in like frozen cloth boots? Come on due, the Romans figured this shit out millennia before this.
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