Is the planet roughly Earth sized?
Can people circumnavigate the globe on land or are there any oceans in the way?
How fast can they move? With even simple railroads, they could cover the distance between terminators in a few weeks, and, more importantly, bring a lot of harvest or farm equipment with them.
How hard does the surface freeze over a 4.5-year night? This defines how close they can get to the dawn terminator before encountering ground too frozen to farm.
How fast can they raise a crop? A party arriving at the frost terminator (aka thaw line, just behind the dawn terminator) would need enough food on hand to last until the first crop came in.
The simplest strategy seems to be for each family or village to settle down at the frost terminator and raise as much food as possible during the nearly 4.5 years of sunlight. When overtaken by sunset, they would up stakes, migrate all the way to the frost terminator, and start over. Given about 4 years, they certainly should be able to preserve and store enough food to last through the migration and ripening of the first crop.
To this simple strategy we add trade. As people spread out across the globe, the arable land becomes filled with farms and farmers, plus a constant trickle of migrants passing through on their way West from the sunset terminator to the thaw line. Now, instead of everyone individually saving food for 4 years, the farmers could help feed the migrants on the way, and stake them to enough supplies to bring in their first crops.
The settled farmers would also maintain the railroads and other infrastructure, both for their own use, and to speed the migrants' passage.
All this would require a great deal of trust, a sophisticated market and accounting system, and universal faith that the migrants would, in turn, become settled farmers who would work off their passage debt by maintaining the railroads and hostels, and feeding all the new migrants.
When nationalism finally did arise, the territory of each country would look like two stripes, running north and south, on opposite sides of the globe.
The most common aphorism for an insane, ill-advised, doomed venture would be "migrating East". The best stories written about this world will probably be about protagonists who are, in one way or another, migrating East.