Travel Light by Naomi Mitchison

You could travel light. Halla is the daughter of a king, cast out as a baby into a world of danger and enchantment. She is raised by bears, lives amongst dragons, converses with Valkyries and avoids warmongering heroes.

But times are changing, and an encounter with the Wanderer, Odin All-Father, finds her at a crossroads. Cutting a fold from his night-blue cloak and laying it over her shoulders, the Wanderer sends her on a journey into the unknown. With only her bear-like kindness, her dragonish wisdom and her own fierce spirit to guide her, Halla must forge her own path .