Owosso 10 Day Weather. Thursday:The Owosso forecast for Aug 24 is 64 degrees and Overcast. Friday:The Owosso forecast for Aug 25 is 69 degrees and Sunny. Saturday:The Owosso forecast for Aug 26 is 68 degrees and Sunny. Sunday:The Owosso forecast for Aug 27 is 69 degrees and Partly cloudy.