The early part of the route was at the edge of marshland in 1066. Much of the army probably followed the high ground along the Escrick moraine, which is now the A19. Others probably went nearer the river where there was more firm ground.
But this is the shortest route and ideal for the 50 year old King Harald. He probably turned left just before the main battlefield as he wanted to keep out of sight. Harald was a very cunning soldier. You can discover why he did this when you get to Fulford.