Yes, they did. Especially the ladies' tall, elaborate headdresses anyways. They were notorious for mice, who felt those humongous wigs were just perfect for nesting. (There were even extremely elaborate women's wigs that had real food, fruit and such, that would also attract bugs--roaches.) No joking. Grr-oss! Some wigs actually had real bird cages in them. Again, not joking!
Actually, one of the things that bugged me about the Collinses of 1790's, was that not one of the ladies, not even Countess Dupree, had a wig on. A French courtesan would never have gone wigless. Naomi would have had one too, with her fashion-consciousness. The spinster sister, perhaps not. She would have seen wigwearing as the sin of vanity. Millicent, the heiress from New York, would certainly have been be-wigged and be-powdered.
The men are another story. It bugs, absolutely bugs, that NO ONE had a pony tail! Men DID NOT have short hair in the 1700's (unless their head was shaved for a medical reason, like scarlet fever). And at least the older, rich men would have had a powdered wig. The Collinses were people of the world. They have been living in a backwater little port town in Maine, but they were still rich and influential people, and they should have had wigs!
Oh well, I guess this would have cost extra money that show did not have. They were too busy spending money on special effects!