Apparently, the militia were better equipped than the regular army to withstand the weather. Washington was able to write Congress on the 27th that "A part of the Delaware militia are stationed [at Head of Elk about six miles north of the British camp]; and about nine Hundred more from Pennsylvania are now on the march that way."
The Delaware militia were formed by counties. They mustered under orders from the State of Delaware and its President. If the Congress's Continental Army and its Commander-in-Chief were in the neighborhood, they were supposed to cooperate. Fortunately, in August, 1777, that's what they were doing.
Even before Washington's arrival in Wilmington, President McKinly of Delaware had ordered the Kent and New Castle militia to march "to such places as may be most necessary to annoy the Enemy and prevent them from plundering the inhabitants." The Sussex militia, meanwhile, were instructed to stay in Sussex "for the defence thereof against internal foes & depredations of the enemy." Translation: Loyalists were numerous in Sussex County. The Sussex militia were to prevent Sussex Loyalists from giving aid and comfort to the enemy.
Washington added his own urgent instructions to McKinley's and he reported to Congress that "There are a quantity of public and private stores at the Head of Elk, which I am afraid will fall into the Enemy's hands, if they advance quickly; among others, there is a considerable parcel of salt."