Can you link to any of the paintings you're thinking of? In the 18th century the vast majority of men in European countries and America wore a peruke AKA a wig. So, if you had curly hair, or straight hair, it didn't really matter, you would wear someone else's hair! Hair on wigs was arranged and curled with curling irons and other heat-based methods. There were many styles you could use for your wig, like this pretty popular picture shows. Typically your hair was kept pretty short under your wig, like a buzz cut.

Some men did wear their own hair, George Washington's hair is his own, and there's paintings of Farinelli where he's got both wigs and his own hair, he seemed to prefer his own hair when he was younger but switched to wigs when he got older. Here's a picture of his natural hair, it's been powdered (I think with colored powder, not white) and styled, it's visibly curly, but I don't know if his hair was naturally curly or it's been curled with tongs.

Also, if you have long naturally lightly curly or wavy hair the weight of the hair usually pulls most of the curl out at the top of your head, so it's only curly at the bottom. Some of the long haired men that have pretty straight-looking hair in pictures may have been more curly-looking at a shorter cut.