Hoshinoya is definitely an upscale group, probably not classic luxury, but upscale in Japan can often provide better service than luxury in other countries.

Non-fir forests that are lush and green are unlikely in March in Japan. Best chance would be to look in Kyushu. There are well-known onsen resort towns in Kyushu, but I don't have any knowledge of which ones are good and which aren't.

Fir forests will be too cold then, it's the tail end of ski season.

If you want to stay near Tokyo, consider the Izu Peninsula. There is a discussion of onsen in the Izu area if you search the Japan forum.

Even if you are willing to try a futon for sleeping, be sure to confirm that the room you are getting has western-style toilet facilities, that's quite common but definitely not universal.