Wigs are still (just barely) fashionable for men at this time. They are going out of style, however. It's most common with the older group of men, not only because it's more the style they are accustomed to, but also because they are far more likely to be suffering from hair loss. Thomas Jefferson wore a wig occasionally, but did not shave his head to do so. George Washington never wore wigs, styling his own hair instead, though he bought wigs for his household servants as part of their uniform.

The wearing of a wig can certainly be attributed to fashion, but many men did wear their own hair. A wig means less time to worry about styling or keeping up your hair, as well as no worries about hair loss issues. If not wearing a wig, but having a head shaved for one, gentlemen would often wear a negligee cap or work cap instead. Work caps are also worn by tradesmen who keep their own hair as a way to keep it clean and free from dust and smoke. Wrapping a kerchief about the head "a la turque" was also popular.

Wigs could be had both cheap and expensive depending on what was desired. There was even a second-hand wig market in London, though I can honestly say that sounds less than pleasant. Ready-made wigs were much cheaper than custom, though more likely to be ill-fit. Another option were hair pieces or even half-wigs. The braid in back, called a queue, could be on a string that tied around the head. With the hair brushed over the string and into the false piece it saved the wearer from the expense of a wig and the difficulties of keeping their own hair long. Wig bags were another option.

/u/colevintage has commented on the subject of civilian fashions at the time, but one of the most egregious errors in the series was the depiction of the British soldiers in the first episode wearing very bad looking white wigs. Soldiers would wear their hair dressed, either clubbed, queued, or plaited, and occasionally powdered. However, wigs were uncommon amongst officers, and would be worn only in very exceptional circumstances amongst men.

Wigs were not without their defenders- namely the widely read Marshal Saxe- who recommended the wearing of wigs from merino wool over cropped hair, While British troops followed Saxe's advice, viz. cropped hair, both in the French and Indian War and in the American Revolution, I know of no evidence which suggests the wiggish recomendation was ever taken up.

For further reading, see:

Cuthbertson, Bennet. System for the Maintenance of a Battalion of Infantry

Simes, Thomas. The Military Guide for Young Officers.

It was, and still is (at least in the British legal system) considered a sign of authority and statesmenship, and in fact the Speaker of the House of Commons still wore a wig while presiding till 1992. Now the wig is largely relegated to ceremonial occasions.

The revival of the wig in the 17th century was believed to be partly caused by the spread of the plague and accompanying hairlice, which were considered traits of the lower classes. This was also the age of 'Artifice', where artificial perfection was valued over 'natural' beauty, hence the powdered, pale skin of the upper classes in contrast to the tanned skin of the working class and rising middle and artisan classes.

The patronage of the arts which grew during this time also helped, as theatre troupes would wear exaggerated costumes using wigs, makeup and other affectations, which were often adapted into fashion.

Chambers, E. K. The Elizabethan Stage is good for some of this, to draw a personal conclusion, I suspect the weakening of the nobility during the war of the roses lead to a more centralized and ceremonialized government, all following the fashion of the monarch, compared to the more decentralized, localized system that held sway before this time.

Also, if you've read any elizabethan and metaphysical poets you'll notice the focus on the artifice, descriptions of 'wiry hair', pale skin, etc: http://www.shakespeares-sonnets.com/sonnet/130

edits: spelling and a few details of eras