The purported death toll of 28,000 is not undisputed. English parishes did not begin keeping records of births and deaths until the mid-sixteenth century, so it is impossible to conduct a broad survey of written evidence. All we have to go by is estimates from individual sources. The Annales Rerum Anglicarum does go for a lower estimate of 9,000 dead, and this is preferred by some prominent historians, in particular Charles Ross. Gregory's Chronicle claims 35,000 dead, while the sixteenth century Chronicle of Edward Hall provides the implausible precise figure of 36,776. In addition to these chronicle accounts, we also have letters from the time of the Battle. The Bishops of Exeter, Salisbury, and Elphin all wrote seperately to the Papal Legate, giving him a figure of 28,000 dead. The Milanese ambassador to France informed his masters in Milan that 20,000 Lancastrians died in addition to 8,000 Yorkists. He later confirmed this count in a further letter to the Duke of Milan, stating that the dead were counted by heralds after the battle, as was customary in Western Europe. Perhaps most usefully, Edward IV wrote a letter to his mother after the Battle, a letter that was delivered and seen by one William Paston, whose family's personal letters have survived to this day. William writes to his brother, John, stating that Edward's letter claimed that 20,000 Lancastrians had been killed. Evidently, 28,000 was the 'official count'. This would seem incredibly high, but it should be noted that contemporary accounts of casualties in Wars of the Roses battles usually tend to provide entirely realistic figures.
Mass graves were dug at Towton, but Richard III had the bodies reburied elsewhere. In contrast to the Yorkists of 1461, Richard's powerbase was in the North. He began building a chapel at Towton (never completed) in memoriam for the dead, who were mostly Northerners fighting for the Lancastrians. One mass grave certainly did remain undisturbed, however, as it was accidentally discovered by builders in 1996. The pit contained 38 skeletons. From the pattern of injuries to the skulls and forearms it is apparent that many were unarmed when they were killed, meaning that they were killed while trying to flee or even as prisoners. The snowy weather made it difficult to run, and the Cock Beck and River Wharfe (a bridge over which collapsed from the weight of routing men) blocked those attempting to escape. The routing Lancastrians would almost all be on foot, whereas the Yorkists could mount for the pursuit. It therefore make sense that casualties should be very high, though it also makes sense that some historians are sceptical of the official death toll.
What historians do tend to agree on, however, is that over 50,000 men were at the battle. This is an extraordinary number by the standards of the Wars of the Roses. Most English armies of the time were raised primarily through retaining and through indenture. The former, a practice termed 'livery and maintenance' involved a lord giving his badge, and therefore protection, to a man. This man might be a servant or soldier in the lord's personal household, but he also might be a knight, esquire, townsman, or yeoman. This protection meant that liveried men could commit crimes with impunity, as the local magnate would ensure that they were safe from the (relatively short) arm of the law. That said, it also protected liveried men from criminal acts. In exchange, liveried men would serve their lords as soldiers when called upon. More troops were raised by indenture. An indenture could simply be an informal, unwritten contract by which an individual tenant would serve his lord as a soldier when needed. There were also written indentures by which lords agreed to give members of the gentry the money needed to raise dozens or even hundreds of troops. In some battles of the Wars of the Roses, almost all the troops were raised through retaining and indenture. But to raise the 50-60,000 troops who fought at Towton, a different mechanism needed to be used. This was the Commissions of Array, effectively conscription orders issued to local magnates. This was not the only time that Commissions of Array were issued during the Wars of the Roses, but the scale was remarkable; Edward issued them for 32 counties, including some dominated by Lancastrians. By the fifteenth century, serfs were not 'typical' in England. Beginning in the thirteenth century, landowners had increasingly realised that it was often more profitable to charge rents rather than make use of customary labour services, so many had freed their villeins and made them paying tenants. Villeins were, by now, very much the minority of peasants. Moreover, they were often the least well-fed and the least well-armed, hardly making them a recruitment priority for Commissioners. This is not to say that there were no 'serfs' at Towton, but they would have been a very small minority of the total. You should not mistake those levied by the Commissions of Array for half-starved conscripts driven into battle at sword-point. All soldiers under the King's banner were paid (at least in theory), and had been since the 1340s. This meant that armies cost a great deal to maintain, raising the question of why Edward and Margaret raised such large forces. Sieges played very little part in the Wars of the Roses, a conflict characterised by a small number of major battles. This wasn't like the Hundred Years War, when ruling a region meant controlling its strongholds. The people of England would generally accept as king whomever could act as king. Holing up in the castles effectively meant ceding all authority to your enemy. As such, no one expected a long campaign and the leaders were eager to amass as strong an army as they could for the decisive clash they knew would come.
As noted, the soldiers at the Battle of Towton were primarily raised through systems of legal and social obligation. This is not to say that everyone was reluctant though. Some men would have been eager to earn a soldier's wage for a few weeks, and hoped to plunder their dead enemies. In the Hundred Years War, English kings had not struggled to recruit thousands of volunteers. But your question related to 'policies'. In this case, there isn't really much to say. Once he became king, Edward IV certainly had policies that changed the nature of government and economy in England, that said, these were more reactions and adaptions to developments, rather than part of any Yorkist manifesto in 1461. That said, there definitely were manifestoes issued during the Wars of the Roses, such as that issued by Warwick and Clarence in 1469, although we lack surviving record of one from the time of Towton. These manifestoes tend to contain similar sentiment even if the specifics vary. The main points are typically reminiscent of a centre-right political platform today: taxes are too high and there is too much crime. They also might cover specific cases in which the King was deemed to treat some nobles too harshly and others too favourably. The early Yorkists under Edward's father certainly placed great emphasis on England losing the Hundred Years War, and this would have remained an issue for those who had served in France, or had benefitted from trade with England's French possessions. Medieval and even early modern English political manifestoes typically attributed problems to same supposed cause: the King was taking advice from the wrong people ('evil counsellors'). In 1461, the attribution of blame was slightly different. For the Yorkists, Henry VI had pursued so many bad policies that he was not fit to be King. But the approach was two-pronged: not only was Henry a bad king, he was also an illegitimate king, because Edward had a better dynastic claim. Now, the Yorkists didn't suddenly decide to overthrow Henry because they realised the House of York had a better dynastic claim. Richard II had been overthrown (within living memory) despite everyone knowing that no one had a better claim. Nonetheless, the dynastic claim was a very important justification, not least because Henry VI, while incompetent, was not identifiably tyrannical in the way that Richard II and Edward II had been. For the Lancastrians, Henry was the rightful and anointed King. The Yorkists saw themselves as being provoked into action, but to their enemies they were ambitious aggressors.