I dont' know about the icelandic. His face may show some of that, but his body does't seem that way to me at all.
IN any case, regarding his movement and difficulty in getting him moving and staying moveing:
You don't know what his training level is, do you? He may be very , very green and have very little experience with a rider on his back, or having a bit in his mouth. Am I wrong in this assumption?
In any case, he looked uncomfortable moving iwth the rider on board. He may just need conditioning, or a check on the saddle fit. But please do some work with him on the ground to better asses his training level before you start riding much.
He does have a very nice walk and really strides out and though he wants to stop , he does't look seriously worried and seems to have a good temperament. Just seems a bit green so I might be a bit cautious with him.
Congrats on your new baby. I am still wearing the baby fat; 16 years later!