Peak of the RV snowbird migration east of the Mississippi is btween Christmas and first week of January, to Gulf Coast and Florida destinations. Permanent home snowbirds in Florida (by far the majority) tend to move earlier. My brother goes to his Florida house end of August.
But most RV snowbird destinations in Florida are still too hot for outdoor life much before October.
There's a different trend for the Texas and Arizona RV snowbird destinations. To Texas, particularly, the move is gradual, following the autumn weather through the southern part of the Plains. A lot of people will be in the Arkansas River basin September-October, move to central Texas or Hill Country and San Antonio, moving down to the RGV when Texas gets colder January and February.