Edward, the second Duke of York (as the rascal became in 1402) had a fair amount of involvement in the Welsh wars, indeed it was during this period that he served the bulk of his career as a soldier. His younger brother, Richard of Conisbrough, was also active for at least a time.
In some ways it's surprising that Henry IV trusted Edward with any military (or indeed administrative) power, but, as in the case of Richard III and Lord Stanley, it's likely the case that Edward was just too big a player to be ignored. From 1402 he was England's only duke, and remained so until Thomas of Lancaster (Henry IV's second son) was created Duke of Clarence in the twilight days of the reign. Rank and blood meant a great deal.
What Edward's personal policy was in those days is hard to discern. He was widely mistrusted, that's for sure, and was repeatedly accused of being involved in treason, notably after the Battle of Shrewsbury, where he did not show up. His alleged participation in his sister's plot of 1405 led to a period of imprisonment and forfeiture but, as ever, Edward came out smelling of roses and within a few weeks of his release was actually opening Parliament on his sickly cousin's behalf.
The experience does seemed to have cured any interest he had in supporting the Mortimer claim to the throne, and after this point he becomes a partisan of the Prince of Wales, and appears to support the future Henry V right through to his (York's) death at Agincourt. Not a bad move, politically speaking.
York acted as a lieutenant of the Prince during the latter's campaigns in Wales in the latter half of the reign, and the Prince was suitably grateful. Following the failure of a campaign to capture the castle of Aberystwyth, Edward was once again accused of treason, but kneeling to the King before the Parliament of December 1407 the Prince 'spoke some generous words of the Duke of York, whose good advice and counsel, he said, had rescued the whole expedition from great peril and desolation.' From such a source this is praise indeed!