It mostly comes down to heavier textiles and layering, either within a garment by quilting or lining, or with multiple garments. For example, a man might put on a shirt, wool stockings, under-drawers of linen, heavier wool breeches, a flannel under-waistcoat, heavy sleeved waistcoat (maybe quilted), a wool coat lined in a thicker fabric, a knit or wool felt hat, scarf or kerchief, gloves, and finally a great coat or cloak. Other accessories could be added such as gaiters to cover the legs further.

Women could have a shift, wool stockings, stays, underpetticoats (which could be quilted or flannel), an exterior petticoat of wool, a quilted waistcoat, a heavy gown, one or more kerchiefs around the neck area, mitts, muff, a cap, possibly another kerchief about the head, and a cloak. They might have also worn breeches or drawers under the petticoats, but this isn't something that was discussed commonly.

Some garments might be cut a bit looser to accommodate layering underneath, but they'll still appear the same style. Generally the solution is the same as we have today- just keep putting on more clothing. New Englanders were known for their love of wool as well. Benjamin Franklin mentions it in a examination he has with the British House of Commons in 1766, saying that in the northern colonies they decided to slaughter very few lambs that previous year so as to have enough sheep to produce their own wool. Likely they still wouldn't have had enough supply for the demand, but it would have been a noted dissent either way.