My husband and I own 50 acres of property. There is a private road
with about 10 or 12 houses on it that butts up to our 50
acres. We have some friends that live on that road (in Argentine
Township, Genesee County, Michigan) and we visit them on occasion on
our golf cart.  Today, a lady who
lives on the private  road came out and told me that I couldn't be on
that road because it was private. I explained that we owned that
acreage that the road dead ends on (in a circle), and she was quite rude in telling
me not to come back.
So, here is my question: Am I allowed to run on, walk on or ride my
golf cart with my children on a private road in Genesee County,
Michigan? This road intersects our county road that we live on and pay
taxes on. Help!

If the road is private, who owns it?  If the lady does, she is within
her rights.  If it belongs to the owners whose property are along the
road, tell her to go stick her head where the sun don't shine.

Some info may be useful here:
http://www.ght.org/OnlineResources/Ordinances/Ordinance%20%23262%20-%20Private%20Roads%20and%20Driveways%20Ordinance.pdf

The owner of the road has the right to limit the travel of the road. 
However, there may also be an easement of record that allows a right
of way.  In order to find that out, you would have to search the
county records.  If that doesn't exist, then there may be a
prescriptive easement (not of record) that allows travel to and from
property.

ilmag

I would try to be more polite than Nelson suggests; the lady may be
speaking for some of her neighbors too.  Ask your friends how the road
maintenance is handled, if there is a homeowners association that
could give you permission, although this is taking the most polite
route.  Probably they just have a common maintenance agreement.  A
private road is not for the exclusive use of the owners unless there
is a sign to that effect.  Usually it is just a road that is not in
the public domain, not maintained by the county.  Landog's link for
Grand Haven suggests that your township may have a similar regulation.
 If it is identical, since your property abuts the road, you are
justified in using it.

If you have friends that live on the road in question, presumably they
can give you permission to ride on it.  It's their road too.  No
problem there.  Also, if the road dead ends on your property and you
don't have another way out (but it sounds like you do), you'd probably
have an easement which is just a thing that says people can't make you
come and go by helicopter.  You have to have a way out.  No problem
there either.  If you have no real friends and you have another way
out, then an owner of a private road can almost certainly tell you to
stay out.  However, it sounds like you just have a grouchy lady who
either needs some homemade cookies and a contrived apology for
bothering her with a promise to try to be more considerate while you
continue to use the road or you ignore her or you tell her to leave
you alone.  Good luck.