Between Winter and Spring, about two months long...a season of never ending wind, NEVER too strong and NEVER too weak. Winds would usually blow at about 5-25 MPH, never faster.
Temperatures would be up to 32 degrees Fahrenheit cooler than Summer but never more than 15 degrees Fahrenheit cooler than an average Spring day for the region.
The name of this somewhat pleasant season, which is intended to transition you slowly into Spring, and THEN into Summer would be called Bluster.
Rainfall would be unchanged, but would likely be blown around the world until the storm died out. Some regions might get more rain, some might get less. I'm not gonna crunch numbers for that, but you get the point.