The river is expected to reach near flood stage by early next week in towns such as Canton, Hannibal, Louisiana, Clarksville and Winfield.
Thunderstorms could bring tornado warnings, hail and strong wind, the National Weather Service said.
The National Weather Service is predicting a wide range of severe weather for Tuesday.
A spring storm has caused scattered flooding, power outages and hail and wind damage in Missouri.
Last spring's allergy season was the worst in 37 years, and this season could be worse yet. Extra moisture in the soil is sending allergen-producing plants into overdrive.
The low temperature of 65 degrees in Columbia broke the previous high minimum of 62 set in 2001, according to the National Weather Service in St. Louis.
On Saturday, temperatures in Columbia reached 89 degrees, matching the record high recorded April 3.
The high of 89 degrees broke the record set in 1978.
Snow started falling 20 minutes before this year's first outdoor Columbia Farmers' Market was scheduled to close.
The National Weather Service in St. Louis advised that Columbia could see up to 3 inches of snow, putting it in reach of an all-time record for annual snowfall.
This weekend's snowy forecast could make this July to June period the snowiest on record in Columbia.
Because Missouri's recent snowstorm was declared a disaster by President Barack Obama, the state can now seek federal aid for the costs the snowstorm imposed on the city.
Most homeowner policies don't cover flood damage and people must buy the coverage through the National Flood Insurance Program.
The 6 inches of snow helped the 2010-2011 season climb to second place on the all-time list for most snowfall from July to June.
Columbia's seasonal total reached 50.6 inches Monday morning. The record is 54.8 inches in 1977-1978.
Columbia and some surrounding areas received between 3 and 5.5 inches overnight.
The snow isn't expected to last long, as temperatures should reach 70 by Thursday.
MU weather expert Tony Lupo says Columbia residents can expect a spring with less severe weather than normal.
Two separate electrical problems caused power outages on different sides of Columbia early Sunday afternoon and in the early hours of Monday.
Strong winds and tornado conditions caused widespread damage as a fast-moving storm whipped through Missouri.