The vision that most of us have of the Puritans, and the Pilgrims, was created by artists in the 19th century. You know, neatly clean-shaven with tall hats with buckles on them, that sort of thing. And if you're a kid drawing a Thanksgiving in colonial Massachusetts, picturing them like that is fine. In fact, I kind of like that. I would be disappointed if a kid didn't draw the stereotypical clothing, hats, etc.
But if you really want to know what the Puritans looked like, all you have to do is to look at ordinary English folk from the 17th century. Even though my family lived in America, they were still English. Ships went back and forth from Boston to London all of the time. Stores in America were stocked with English goods. They wore ordinary English clothing. Shaving in the 17th century wasn't as easy as it is today, so a fair amount of the men had beards. And long hair didn't mean that you played in a band, it just meant that cutting hair was a nuisance in those days, too.
Of course, if you look at formal portraits, like the one here of Increase Mather, you are not seeing a common man. And I daresay you aren't seeing what Reverend Mather looked like on an everyday basis.
If you want to know what my family, the Puritans, looked like, just look for a typical crowd scene during a performance by William Shakespeare. And yes, most had beards, at least the men.