I cannot answer your question about the limits of Icelandic horses in dressage. I can provide some data about how my individual Icelandic is performing in his introduction to dressage. I did not start riding until my late 40s and got my first horse, an Icelandic named Blessi (Veigar fra Budardal) when I turned 50. Since I was new to riding, Blessi and I have gotten regular dressage lessons--mainly to improve my balance and knowledge of the aids. We also get tolt riding lessons. My Icelandic instructor incorporated basic dressage--shoulder in, collected trot and canter, etc., as part of Blessi's tolt training (which is not ridden in a collected way in Blessi's case). My Icelandic instructor moved out of the area so I have been taking lessons with an open minded dressage instructor who is adapting her training methods to Blessi's confirmation.
My instructor Danielle rode Blessi at his first dressage test (non-gaited) at a local level B, schooling show over the weekend. They did the introductory level A & B (walk-trot). The judge was an A level judge and we had no idea how she would score a short legged, thick necked, furry pony. They took blue ribbons in both classes, scoring a 68.5 and a 72.0. The 72.0 represents the third highest score of the entire show. The highest score was 72.8 at this show. Danelle and Blessi scored a 9 out 10 for movement 7 (trotting a right circle). We were thrilled with these results.
Here is a link to a video of his performance:
So I can say without a doubt that an Icelandic can do a very nice job at a local level in dressage with training. The dressage instructors with whom I have spoken predict that if he continues with his training, Blessi can do a credible job up to third level.
Just some data for your consideration. Oh, and you need to find an open minded, adaptable dressage instructor. The first dressage instructor to whom I took Blessi said that he was untrainable--she could not get him to accept the bit, his trot was impure, and the tolt was an abomination. Blessi had his revenge over the weekend.
I am not sure where you live but I would recommend that you and your Icelandics try riding in an open dressage competition. I just need to get up my nerve to try it myself. Blessi and Danelle set the bar very high.
Oh, and I forgot to mention, that the more collected work we do at the trot and canter, the better Blessi tolts. The dressage exercises really strengthen his hindquarters.