This doesn't really meet your criterion for what you had in mind but from my own personal experiences I found that the Sapporo Snow Festival in Hokkaido during early February is fantastic for ambiance and as close to a "romantic" feeling as I have ever experienced when I was with a lady friend. The ice structures illuminated at night are rather beautiful to behold and despite it being in the middle of winter, at night, and in Hokkaido... the numbing cold you might expect isn't that bad actually. The general mood is festive and the locals are very accommodating.
From Sapporo you could travel to Noboribetsu which is famous for its hot springs. And if you had the time and inclination, Otaru has some pretty good seafood, worth the trip imo. Yubari has some nice slopes if skiing is your thing as well. Mount Racey is a very nice resort hotel despite basically being in the middle of a mountainous country town, heh. All locations (Sapporo, Noboribetsu, Otaru, and Yubari) are relatively close and can be commuted rather easily. Just a suggestion anyways if you were open to itinerary ideas. Whatever you decide, best of luck and have a wonderful trip.
SAPPORO SNOW FESTIVAL
Noboribetsu travel guide - Wikitravel
Noboribetsu Grand Hotel (Noboribetsu, Japan) - Onsen Hotel Reviews - TripAdvisor
Otaru-Shi, Japan Vacations, Tourism, Guides, Hotels, Things to Do, Restaurants - Yahoo! Travel
Yubari Resort: Hotel Mount Racey
Hotel Mount Racey (Yubari, Japan) - Onsen Hotel Reviews - TripAdvisor