There is such thing as a vegetarian hot dog. It's disgusting, but it does exist. But then again, we've got to realize that all these ponies we love live (at least mostly) on a diet of hay, grass, and flowers, which are disgusting to humans but probably like bread and butter to them. So it's possible that veggie dogs might be a common food in Equestria. But that doesn't explain Applejack's ham sandwich...
Assuming that AJ's sandwich really did contain meat, that must mean that ponies keep some kind of livestock. A barn inhabited with cows was briefly shown, which implies that ponies have enslaved cows and keep them for milk - and presumably, meat. It's a disturbing thought considering that ponies are technically herbivores, and seeing how their world lacks war, hate, and racial prejudice, but I see this as the most rational explanation for the ham sandwich (and probably the hot dogs, too).
If it wasn't for the sandwich, I would've chalked the hot dogs up to Pinkie's general insanity. But looking deeper into it, ponies in general may not be as nice as we think...