Travelling to their destination town takes about 3 months by horse cart.
Also, the magic school was located in the north of the Fairy Human Continent (the continent where the main inhabitants are Humans and Fairies. The orphanage is also in the Fairy Human Continent.)
So there is a lot of snow piled up.
The reason they set off in summer, is in order to arrive at the magic school before snow falls for real.
"Lute-kun, are you sure you won't come to the magician school with me? There is an Adventurers' Guild at the town near the magic school, I will support us both by earning our living expenses."
"Support huh…… I don't want to be a dependent."