This is a Disney Junior series that I'm rather fond of. In this one, a big ol' storm of dust and tumbleweeds messes up the town of Nice and Friendly Corners. The dust causes a lot of a mess and few sneezes. We've got one from Sheriff Callie's horse, Sparky, another from Peck's mule, Clementine, and another from Toby, who is, well, an anthropomorphic cactus. So, yeah, technically a plant, but hey, we've done turtles and dragons before, so why not, right?
https://www.youtube.com/watch?v=SgRNrzfZ7mw - the actual video is shrunk to a portion of the screen, presumably to defeat YouTube's copyright detection. There may be other videos - I saw one that was labeled as this story, but wasn't actually it. It's also currently available in full, proper HD-quality for free on the Disney Junior app, for those that have access to it.
On the YouTube video:
9:38 - Toby
12:00 - Sparky
12:07 - Clementine
