Having a representative form of government meant that people had to gather together to review and alter the laws, to settle disputes through the courts and to renew and forge new alliances. These gatherings (or "Things") must have seen large numbers of people, and larger numbers of their horses, convening through the passes and over the plains.
The tradition of riding with a free running herd of remounts hasn't ended. On a long tour that covers a lot of distance each day a rider will ride up to 3 horses during that day. We think that some of the wonderful willingness most Icelandics exhibit is based on this. They sort of know that they won't be working all day long and most of the day will be spent running free with the herd so they might just be a bit more willing to work hard for their riders.