A major problem with incorporating different seasons on Arthur is continuity. For example, like Ladonna, Sue Ellen moved to Elwood City during the winter when Arthur was in the 3rd grade. But then we see Sue Ellen in episodes that take place prior to that winter ("Arthur's Eyes" is the most obvious).
When it comes to continuity, the summer episodes are the most troublesome. According to "Arthur's Faraway Friend," Buster was supposed to return in August. But most of the episodes where Buster was traveling with his dad, the kids were in school! Oh, yeah, and then there's D.W.'s snowball. In the summer she always checked on it, but with episodes like "The Blizzard" and "Return of the Snowball," the timeline is messed up.
If Arthur were set during the summertime, like Phineas and Ferb, that would be great! But what will become of Mr. Ratburn? Please don't have anyone go through Summer School!