Not a lot of great news in the short-term. The wet pattern so far this year is likely to persist into March as an active weather pattern from the Pacific Ocean moves across the U.S.
In addition, the temperature gradient is amplified more than normal this late winter into early spring meaning colder north and warmer south. This will help fuel the storms and keep things active.
The outlook for March calls for temperatures near or slightly below normal with precipitation above normal.
The outlook through May calls for near normal temperatures and near to above normal rainfall.
The two week rainfall graphic from the NOAA/NWS/Ohio River Forecast Center calls for 1.5 to 3.0 inches of rain across the state of Ohio. Normal is about 1.5 inches so expect above normal precipitation the next several weeks. The greatest totals the next 2 weeks will be in the southern and western sections of the state. Precipitation will begin to increase starting later this week.
All indications are the last freeze this freeze will be normal or a little later than normal. Hence, expect 2 and 4 inch soil temperatures to lag behind normal at least through April.
On another topic, if you think overall it has been wet, it has. The last 10 years is the wettest on record since 1895 in Ohio. The attached graphic shows the 24-month running average precipitation index for Ohio, provided by the NOAA Midwest Regional Climate Center. It shows even the drought in 2012 was not enough to turn the index negative for a 24-month period. You have to go back to the 2008/2009 period to see the last time the index was negative. No other time since 1895 has the index been positive for so long. Looking deeper at the data it does show northwest Ohio has seen the index drop briefly negative a few times over the last 10 years while southern areas have been all positive. Bottom line, it has been wet overall for quite a long time now.