Hair is not personally property until it is removed from your body, it is just part of your body, just like your nose or your femur.
After it is removed from your body, it is the property of the person it used to be attached to, although it is frequently promptly abandoned to a trash bin or the floor of a hair cutter.
A married woman in Michigan is not now required to have her husband's permission to cut her hair (unless the husband has been declared her legal guardian for extraordinary cause due to something like dementia by a court with ample due process protections, in theory, anyway).
This wasn't true even in 1850 and hasn't been true at any time since then.
It may never have been true in Michigan while it was a part of the United States of America, although the state of territorial law under the Northwest Ordinance was not necessarily easy to determine with certainty. Almost certainly, there was never a statute to that effect on the books in Michigan or any preceding U.S. territory.
The 1850 Constitution recognized the right of a married woman to have separate property that was not marital property (not unlike the law of community property states and countries at the time and not unlike states like Colorado).
The 1855 statute, a 1911 statute not linked above, and the 1981 statute essentially put married women on equal footing with single adult women in terms of property ownership and legal status, with the 1981 statute basically just re-codifying the 1855 and 1911 statutes in more modern language.
These legal authorities did so in order to abolish the common law doctrine that upon marriage, a husband and wife become one legal person who acts legally though the husband, called the merger doctrine a.k.a. coverture.
Historical background for this wave of statutes can be found here. Justice Kennedy reviewed the history of this law in his 2015 opinion legalizing same sex marriage nationwide in the United States.
One U.S. state was outside the common law tradition and a laggard, but it wasn't Michigan:
In 1979, Louisiana became the last of the states of the U.S. to have
its Head and Master law struck down. An appeal made it to the Supreme
Court of the United States in 1980, and in the following year the high
court's decision in Kirchberg v. Feenstra effectively declared the
practice of male-rule in marriage unconstitutional, generally favoring
instead a co-administration model.
While these statutes are not directly applicable to the question, they do, more generally, disavow a legal worldview in which one could imagine that a woman would require a man's permission to cut her hair, although this is almost surely just an urban myth. Pre-1850, the government in Michigan, which was basically on the frontier at the time, was just too weak to maintain that kind of control over people.