Tiny purplish flowers on a short stalk of leaves

Yes that's it!!! I have some of it in my garden too.

 

http://www.ppws.vt.edu/scott/weed_id/lamam.htm

http://www.wiseacre-gardens.com/plants/ ... eweed.html

Check out these two sites, the first shows Henbit which is a common weed that shows up in late winter. The second is Bugleweed.

The stem in your second picture appears to be square which is like the Henbit stem and the flowers cluster at the top of the stem and down the stem at each rosette of leaves. Henbit is the first thing that blooms in the yards around here, this year we have had two growths of it. It bloomed in January, dropped seeds and bloomed again in March. It is pretty much gone now and won't show up again until maybe next fall or but definitely late winter.

If the flowers are tall spires, instead of clusters at the end and along the stem, it may be Bugleweed.
Bugleweed's normal bloom time is May - June, it might still be a little cool in Ohio for Bugleweed.

If it is Henbit, it can be invasive in flower beds but I like the looks of it in the yard before the grass greensup. If you want to try to get rid of it, now is too late. You need to use a pre-emergent on it in the fall.

 

Purple Deadnettle is another name for Henbit, I just have always known it as Henbit and really like it.

Some say yes, it's a weed so it must be yanked up or killed and some say why bother.
So I guess it depends on whether you like the look of it, which I do so I leave it alone.
It has a relatively short life span compared to most weeds, warm weather kills it, it doesn't grow back once it has been mowed down, pulls up out of flower beds very easily as opposed to weeds with massive root systems and in late winter is usually the only color you will see in your yard.