The threat posed by the Lancastrian peers in the north was too large to be ignored. In addition, Jasper Tudor, Earl of Pembroke was organising resistance in Wales, and there were various rumours about Queen Margaret. (She had actually sailed from North Wales to Scotland to conclude an alliance with the Scots, one that involved the transfer of Berwick to Scotland. Contrary to Shakespeare, she was not at the Battle of Wakefield, any more than Richard of Gloucester (aged 3) was going around axing people at the first Battle of St. Alban's.
The Earl of March (soon to be Edward IV) was sent off to Shrewsbury to hold Pembroke in check. He was well placed to recruit from the (former) Mortimer lands and undoubtedly attracted support from a range of local gentlemen who feared what they perceived as a 'Welsh' invasion.
His father gathered a force from Kent and the Cinque ports, to which was added some followers from his own southern estates. On 2 December 1460 he left London accompanied by the Earl of Salisbury and his own second son, Edmund of Rutland.
Warwick remained in London to run the shop, no doubt assisted by his intellectual brother Bishop George, the Chancellor. The Yorkists were spread quite thinly, though, and neither York nor March was able to prevent the Earl of Devon moving up from his own country to join the Lancastrian forces in Yorkshire. As far as I can discern, they didn't even try.
York eventually arrived at Sandal on 21 December, having recruited some modest additional support from his supporters among the northern gentry. However he discovered (and he should not really have been that surprised) that his lands and those of the Nevilles in the area had been thoroughly spoiled and plundered by the enemy. He faced superior forces that were in control of Yorkshire and held (among other places) York itself and the powerful stronghold of Pontefract.
To make matters worse he was short of supplies and Sandal had not been stocked against his arrival. It is hard to deny that York seriously underestimated the opposition and made a strategic blunder by attempting to take them on with such a meagre force. (Hindsight makes for great commanders, but it might have been better to take out Devon on his route north, join with March and the Mortimer tenants to settle Pembroke and then attack the main Lancastrian force.)
York was under effective siege at Sandal. There are various accounts of how he was tempted out, and it is sometimes claimed he had negotiated a truce with the Lancastrians, which Somerset broke. In any event, given that he had a supply problem, it's hard to see how he could simply have sat in Sandal indefinitely.
What can be said for sure is that York made a sortie on 30 December and was comprehensively defeated. He and Rutland were killed in the battle and Salisbury, taken alive, was executed at Pontefract next day. (He was unpopular in the area.) Another important casualty was Salisbury's son, Sir Thomas Neville.
It has been suggested that John, Lord Neville of Raby (Exeter's brother-in-law) changed sides at Wakefield, appearing as a reinforcement for York then turning on the duke in the battle. This cannot be ruled out, and might explain York's emergence from the castle. However it is also possible that Neville's colours and badges were mistaken for other Neville reinforcement, perhaps even Warwick. We cannot know, though we can have as many theories as we like. If John Neville was a traitor, he soon paid the price, being one of very many killed at Towton a few weeks later.