The scenario ends: Yorkists win only a 'minor victory' as they have routed the Lancastrians into exile, but Buckingham, Somerset, Queen Margaret & Prince Edward are all still at large. The Lancastrians however, win a 'major victory' as they have killed Richard of York!
Now the Yorkist cause is championed by Edward Plantagenet (previously Earl of March, now Duke of York himself from inheriting his father's title.) His father's death is not such a blow to Yorkist factional hopes, as he historically died just one year later at the tail-end of 1460, at Wakefield. Now the Yorkists are the controlling faction at court, but without the support of the majority of nobles – several of them lost their fathers to Richard of York at his earlier battles of Lutterworth & Lawford Heath, and are in no mood to make up. The Lancastrian cause in exile shall return in 1460 to challenge them, so York must defend all England from invasion, and do it with a small core of loyal & active Yorkists plus a large mass of uncommitted or actively hostile nobles!
(Incidentally, the historical Edward declared himself king Edward IV after his father died, but does not do so in this game. Why? Well, historically Warwick won at Northampton and killed many Lancastrian peers who are still alive in this game; York advanced his hereditary claims to the throne and got Parliament to pass the 'Act of Accord' which named the Yorkist line as heirs after Henry VI (disinheriting Henry's actual son); plus after York was killed the Lancastrians had lost a lot of popularity by plundering and revenge-seeking, while March had won an independent victory at Mortimer's Cross. In other words, the country just isn't ready quite yet for a rival king to Henry VI, and the wars at present are still only for becoming the controlling influence at court. Give it time though, and the increasing bitterness & rivalry will prepare the ground for the Yorkist claim to become overt!)