Now, it's a bit of a misconception that everyone wore wigs in the 17th/18th centuries in Europe, as lots of men (even rich men) did wear their natural hair, and women wore their natural hair with "supplemental" bits of hair only, but if you're a bald man looking to do a little time travelling I really think you can't do much better than Wiggy Mozart-George-Washington-Time. Consider:

• If you wanted to wear a wig and weren't naturally bald, you had to shave your head anyway, so lots of bald guys around.
• When you wig was off you could wear a fun little hat to keep your head warm, which would also look good with your sweet nightshirt and banyan bedtime ensemble.
• Powdering hair was what was up for both wigs and natural hair, and it had to be curled and styled too which took a while, but if you wore a wig, a servant could do a lot of that labor while you were doing something else, then you just plop on your hair and go out!
• Oh and Handel was totes bald under that wig.

This is copy-pasted from an earlier answer I made here, which asked if hairstyles ever affected social class:

Yes--Chinese-American immigrants in Exclusion-era had a heck of a time over their hair.

At the time, keeping your hair in a queue (such as on these fine young men, it's a long braided hairstyle) was considered extremely culturally important, and a disgrace to your family heritage to cut it. This was, of course, the general feeling of the Chinese-American community, but not the American community as a whole. In fact, white Americans considered the style strange, and actually made a bit bigger of a deal of it than should have been necessary.

Here's where the fun starts. In 1876, there was a law passed in California where any housing complex had to have 500 cubic feet of air for anyone living within. People who broke the law had to pay a fine. The law was passed with the intent of running out some Chinese, and, of course, was really only enforced against the Chinese after its passage. When nobody agreed to pay the fine, San Francisco passed an ordinance that required the queue's to be cut to an inch in length.

That caused enough of an uproar that it went to the courts, and in Ho Ah Kow v. Nunan, the Ninth Circuit decided that the law was against the 14th amendment, because it specifically targeted the Chinese, even if it was race-neutral on it's face (don't let that fool you though, the decision was still pretty racist).

As another perspective, the Chinese were aware that their hairstyles made it harder for them to fit into greater society, so they made some effort to hide them. Though we can't know who and who wasn't intentionally hiding their hair, pictures such as this one on an immigrant record seem to show a distinct lack of the queue, as it's hidden behind the back. Obviously it could just be there by chance, but it's also likely that the Chinese were aware of the stigma the queue brought them, and tried to emphasize their American-ness by hiding it for the picture.

Sources:

http://asianhistory.about.com/od/glossaryps/g/What-Is-A-Queue.htm

Anna Pegler-Gordon, “Chinese Exclusion, Photography, and the Development of U.S. Immigration Policy,” American Quarterly 58 (2006): 55-77.

Thomas Wuil Joo, “New "Conspiracy Theory" of the Fourteenth Amendment: Nineteenth Century Chinese Civil Rights Cases and the Development of Substantive Due Process Jurisprudence,” University of San Francisco Law Review 29 (1995): 353-388.

As some of the more knowledgeable might know, shaving with a razor is prohibited in Jewish law. But when everyone around is shaving, who in the hell wants a beard? Jewish law generally interprets the relevant biblical verse as prohibiting shaving with a razor, which allows other shaving methods. Today, this generally means electric razors, which don't operate by the same principles. But what was a religious Jew to do when they wanted to be clean shaven?

Many non-razor methods of beard-trimming were used in the past for this purpose. The most boring is simply to use scissors to cut close to the skin. There were also special creams and powders, which would either essentially burn off the stubs of hair, or, with a knife of scissors, would produce a clean shave without a razor.

Anecdotally, I've heard of students in Jewish boarding schools/yeshiva, who, being young men, were rebellious and used razors. But when a Rabbi walked by, they'd surreptitiously throw a bit of shaving-powder into the air. Apparently it had a distinctive smell, and would thus create the illusion that the students were shaving according to Jewish law. Unfortunately I can't find any solid reference to it, but it's an entertaining thought.

This old NYT article talks about this. Apparently prior to the electric razor's adoption, New York had kosher barbers, who'd shave customers according to Jewish law, using powder and a knife.

One of the more unusual hair fashions that always interested me is the fashion for high foreheads in noble women from around the early 15th century.

The quite excellent Evolution of Fashion by Hill and Bucknell (if you're at all interested in period costume, get this gorgeous book) advises that for ladies of the 1420s, "The front of the head is shaven to create a high forehead." For 1440s costume, the description moves on to "Plucking of the hair to achieve a high forehead, plucking of eyebrows." We can see this quite well in Petrus Christus' 'Portrait of a Young Woman' which has that distinct high forehead and almost invisible eyebrow line which was fashionable at the time. Here is another by Christus with that exaggerated high hairline created by plucking of the hair. It really isn't until the 1500s is underway that we start to see portraits with a more natural hairline appear again, but even the heavy gable head dress of the 1530s as worn by Katherine of Aragon artificially hides the hair all over again.

The Zwan was looking for interesting trivia about baldness in particular

Yes, it was triggered by this shower-thought: have people always been vain about baldness, or is it more of a cultural thing? And if it has been a sensitive topic since the beginning of mankind, does that mean we've had combovers since ancient times too? Is there any writing on that topic? Roman politicians mocking their opponents or that sort of thing?

^(PS: "The Zwan" :D Funny, that was actually the name of the ancestral home in Scheveningen from which my surname is derived)