I am happy enough to entertain that Caldwell might be of Norse origin - Mrs Gordon thought so as well. However bear in mind that the Domesday Book had nothing to do with Scotland. The Ragman's Roll was an Edward I thing when he thought that he could subjugate the Scots by thowing his weight around in a very nasty way in the period before Bruce but AFTER the Caldwell name had been established in Scotland. Edward did more to unite Scots into a sense of nationhood by his actions. The battle of Largs was in 1263 - also after the Caldwell's had appeared. Don't think there were too many prisoners taken. In fact the Norse were allowed ashore to bury their dead and then back to their ships and eventual return to their homelands. Seems a big strange that Norse prisoners might be given land anyway - they would more likely have been treated as slaves. More likely that King Alexander I granted lands to his key supporters in the battle as a reward for services rendered and they were most likely nobles and other landholders especially from the Renfrew and Ayrshire areas.
Harold Hardrada was the Norse King who came to help Tostig (Harold Godwinson's brother) and was trounced by Harald at Stamford Bridge in England just prior to Hastings - he was a Northman not a Norman. "By 1086 there were only two surviving English lords of any account. More than 4,000 thegns had lost their lands and been replaced by a group of less than 200 barons." (Oxford Illustrated History of Great Britain). "In military matters, the harrying of the north durng the winter of 1069-70 also suggests ruthlessness on a new scale about this time." (ibid)
A good number of Anglo-Saxon nobility and other refugees sought sanctury in Scotland. This seems as good a time as any for the Anglo-Saxon name "Cold-Water" to be introduced into Scotland - but surnames were not in general use at that time!
Anglo-Saxon English had already been in use in the Lothians for some time and had also been introduced into the Ayrshire area by the Northumbrian victories of Athelstan and Edmund which resulted in more of a colonisation rather than an occupation, English names were intorduced in the low parts of the country but Gaelic names remained in the higher and more inaccessable parts. Caldwell could be a result of these times.
These arguments help back up David Caldwell's hypothesis of the old-English "Cold-Water" but I still wish to throw around as many other "name" theories that I can dredge up as I am still not 100% convinced. I still favour a generic name for a group of people rather than everyone being descended from an association with a single family estate.
You have also have to be careful not to mix up Norwegians (Norse) and Danes - they at that time were just about as popular with one another as the Scots were with the English.
Norsemen, maybe, Anglo-Saxon's, maybe, followers of the Norman's invited into Scotland, very possible, but I think it more likely to be an extended family, tribe, clan or other identifible group of native Strathclyde British who were given or adopted a name to identify themselves.