I remember the ending being a total bummer but I don’t think the dog COULD have frozen to death with the kid.
But any acquaintance between Ouida and actual fact is purely coincidental. She is all romance, coincidence, and ridiculously tragic endings.
Under Two Flags is probably her most famous story. It was considered very scandalous at the time because the heroine was a "fallen woman," a camp-follower of the French Foreign Legion. Bertie Cecil takes the blame for his wicked brother's forging a note and flees to Algeria to join the Foreign Legion. He loves the widow of a nobleman, whom he cannot woo because he enlisted under a false name. The camp-follower, Cigarette, loves him but her love is not returned. Eventually she leaps in front of a firing squad to save Cecil's life, his name is cleared and he returns to England.
It's the Breathless Romance School of fiction, but it's really quite good. It was a best seller and much liked, especially by British soldiers. Go figure.