Yea but Celtic culture was in mainland Europe in the Bronze Age. Those very small horses are found in the lands of the Celt.
However, I wouldn't discount your theory either. Unfortunately, the evidence to support or disprove it has been lost or is yet to be discovered (perhaps in one of your Irish peat bogs?). It is a fascinating subject.
But we have "small and slender" horses from the Bronze Age with "shoulder heights of 111 cm and 120 cm" that is from about 10.3 hands to about 11.3 hands that is about the average size range of a Caspian and the same type of build too.
the ancestors to our Exmoor and Dartmoor ponies were certainly on the scene by then.
"modern DNA research to date has not supported the traditionally-held view of the origin of the Exmoor pony, as existing studies indicate they share their maternally-inherited mitochondrial DNA with various other horse breeds from across the world, and their paternally-inherited Y-chromosome is identical to that of most other domesticated horses."
Regarding the Dartmoor pony .... "The Dartmoor Pony was used in medieval times for carrying heavy loads of tin from the mines across the moor. It suffered greatly from the infusion of Shetland blood in the years between 1789 and 1832" "The Dartmoor received Arab blood from the stallion Dwarka, foaled in 1922, as well as Dwarka’s son, The Leat. Welsh pony breeding was introduced from the stallion Dinarth Spark, and infusions of Fell Pony blood was also added."
Not Iron Age but New Age.