 If you liked
Shirayuki Hime no Densetsu
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 ...then you might like
Akagami no Shirayuki-hime
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In both these stories, a young maiden flees into the woods, because a vain person wants her, or wants her dead. In the forest, she meets her saviour(s), with whom she lives since then. With her new comrades, she goes through various adventures, and grows as a person.
The maiden's main love interest is a prince, who also falls for the protagonist early in the series. However, the persons who caused the exile of the maiden pose some difficulties, which have to be overcome.
If you want to see stories which are inspired by a certain tale of the Brothers Grimm, both titles may be for you.