On Our Own (1988)
On Our Own is a 1988 family film about four children, Mitch, Kate,
Travis and Lori. After being abandoned by their father and with the
death of their mother they are forced to move into a children's home.
Feared they will have to be separated, they escape to their old home
where Mitch collects all the money he can find, and his Uncle Jack's
address, thinking Jack will know where their father is. They also
manage to get their dog back. They then get into their mother's old
car and drive away, with neighbors spotting them. The police are now
on their trail...(Edited from Wikipedia)
Browse through screenshots here and here. Check out some clips. Or, just watch the whole movie on YouTube :-)
Another possibility is The Beniker Gang (1985), similar in many ways to ''On Our Own''. Except this one features a group of unrelated orphans who, in order to escape from the foster care system, take off on a road trip.
As far as I could make out, the group don't ever travel through snowy terrain. Read a review; browse through some screenshots; two clips here and here. If you want to verify the scenes you mentioned, you might also want to check this link.