Hadn't heard of gin with cranberry, but vodka and cranberry is a fairly popular mixed drink here in the States, sometimes called a "Cape Cod" (presumably because most cranberries in the US are grown in eastern Massachusetts). Often garnished with lemon, just like ClaireBear's "Boggy Delight."

I never thought of serving it hot, but it sounds like an excellent hot toddy. Cranberry is noted for its medicinal properties -- good for any kind of infection.