King Arthur

Arthur (Clive Owen) is portrayed as a Roman cavalry officer, also known as Artorius Castus, the son of a Roman father and a Celtic mother, who commands a unit of Sarmatian auxiliary cavalry in Britain at the close of the Roman occupation in 467 A.D. Arthur is loyal to Rome and a devout Catholic, but follows the teachings of Pelagianism, which many consider heretical. He and his men guard Hadrian's Wall against the Woads, a group of native Britons who are rebels against Roman rule, led by the mysterious Merlin (Stephen Dillane).
As the film begins, Arthur and his remaining knights Lancelot (Ioan Gruffudd), Bors (Ray Winstone), Tristan (Mads Mikkelsen), Gawain (Joel Edgerton), Galahad (Hugh Dancy) and Dagonet (Ray Stevenson) expect to be discharged from their service to the Empire after faithfully fulfilling a fifteen-year commitment.
However, on the night when they are to receive their freedom, Bishop Germanus (Ivano Marescotti) sends them on a final and possibly suicidal mission to rescue an important Roman family. Marius Honorius (Ken Stott) faces impending capture by the invading Saxons, led by their king Cerdic (Stellan SkarsgÃ¥rd) and his son Cynric (Til Schweiger). According to Germanus, Marius' son Alecto is the Pope's favourite godson and may be "destined to be Pope one day".
At the remote estate, Arthur discovers that Marius has immured pagans, including a Woad named Guinevere (Keira Knightley) and a small boy named Lucan. Arthur frees them and decides to take everyone, along with Marius' family, back to Hadrian's Wall.
One night, Guinevere takes Arthur to meet with Merlin, the leader of the Woads and her father. At first, Arthur thinks Guinevere has betrayed him, but Merlin has come in peace. It is revealed in a flashback that Arthur's mother had died in a Woad attack when he was a boy. Arthur's famous sword, Excalibur, had belonged to his father and marked his burial mound. Arthur had pulled it from the mound in an effort to rescue his mother from a burning building. Merlin suggests an alliance between the Woads and the Sarmatian knights against the invading Saxons.
Marius then betrays the group and takes Lucan hostage and attempts to kill Dagonet but is shot by Guinevere with an arrow. While moving on to the south, Alecto informs Arthur that Germanus executed Pelagius after being insulted by his teachings of equality. Tristan returns from scouting the area and tells Arthur that a Saxon army is close behind them. The knights stay behind to hold up the Saxons and allow the refugees to escape. They soon encounter the Saxons at an ice-covered lake bordered on each side by steep cliffs. Greatly outnumbered, Arthur, Guinevere and the knights attempt to repel them with arrows. The battle is won when Dagonet runs to the middle of the ice and breaks it with an axe at the cost of his life. Many Saxons are also killed, and the rest must return the way they came.
Arthur and his men form an alliance with the Woads to fight the Saxons. In the climactic "Battle of Badon Hill" set just south of Hadrian's Wall, the Woads catapult flaming missiles at the Saxon army. When the hosts meet, Guinevere engages in combat with Cynric. Cerdic fights and kills Tristan before facing off with Arthur. Meanwhile, Cynric disarms Guinevere and is engaged by Lancelot. Cynric shoots Lancelot with a Saxon crossbow. Lancelot then throws his sword into Cynric and kills him. Lancelot dies with Guinevere at his side. Arthur kills Cerdic and the Saxons are defeated.
While he realises that his ideal Rome exists only in his dreams, Arthur despairs over the deaths of his men. The film ends with the marriage of Arthur and Guinevere, after which Merlin proclaims him to be their king. United by their defeat of the Saxons and the retreat of the Romans, Arthur promises to lead the Britons against future invaders. Three horses that had belonged to Tristan, Dagonet and Lancelot run free across the landscape, as the closing narrative describes how fallen knights live on in tales passed from generation to generation.

Question: Where do they encounter the Saxons?
Answer: An ice-covered lake