With Fjords you could do Best turned out, Family pony and Foreign breeds. There could be more but this is what my local shows (when I lived in Herts) offered.
My best friend and professional event/dressage rider used to ride a Fjord as a side project and she competed her in dressage, show jumping and one day events. She regularly won Prelim and Novice dressage. She won a 3ft SJ class and was a great little trier across country. Their legs maybe short, but they're as competitive as any other out there.
I have seen Fjords happily competing up to Novice/Elementary dressage, 100/110 cm (Discover/Newcomers) SJ, and eventing up to around BE 100 level, as well as driving competitions. They are versatile allrounders. Due to their build I think it would be hard to compete them in any higher classes (for example, even though they can learn the dressage moves they don't have the athleticism of a WB which would be expected in Medium onwards.) They are also fine for lower end endurance competitions (again, most of the horses competing at top level are specialised breeds), Trec etc.