Owain's followers were a good cross-section of the Welsh population, including many landowners but also a range of lesser folk, as can be seen from subsequent pardons and other documentation. Many Welsh students and labourers reportedly returned home from England to join the rising. He had very broad support among the clergy of Wales, the Grey Friars (notably Ricardian during the early 1400s) being particularly prominent followers.
The motives of these people are not hard to understand - for a beginning, a long suppressed desire for a ruler of Welsh blood, indeed a Welsh state. At a more practical level, they were hard pressed by financial exactions, lived more often or not at the mercy of the corrupt officials of absentee English lords, and were oppressed by laws that treated them virtually as enemy aliens in their own land.
What is perhaps more interesting is the fact that, even from the beginning, Owain attracted a number of English followers. In some cases (especially when he looked like winning) these probably included 'colonists' who wanted to secure their future within an independent Wales. For others though the decision seems to have been a political one, as much rooted in hostility to Henry IV's government as in any interest in 'freedom for Wales'.
Owain was also able to form alliances with English nobles opposed to King Henry, the most obvious cases being the Earl of Northumberland and Sir Edmund Mortimer. Whether these alliances would have survived a victory for the combined opposition it's impossible to know. My guess is that they wouldn't have survived very long.
Conversely, and quite contrary to modern myth, not all the Welsh supported Glyn Dwr. For example, the Welsh tenants of Pool (now Welshpool) remained loyal to the Charlton family throughout the rising, and were subsequently rewarded with an enhanced charter of liberties. Another case is the famous Davy Gam (Dafydd Gam) who remained steadfastly loyal to Bolingbroke (His feudal lord as Lord of Brecon) and was prominent in arms in the King's service against Owain. For many, loyalty to a lord was still more important than loyalty to the concept of a 'nation'.
Unfortunately for Owain, his support was what modern pundits would call 'flaky'. As long as he was successful people flocked to his banner, but as soon as the tide turned decisively against him most hurriedly submitted to Henry and bought pardons.
