Do I need a guide to ride off-piste and tree runs in Japan?

It depends entirely on which resort you're at, which is the part people planning their first trip usually don't expect. Japan doesn't have one off-piste rule; it has as many as there are resorts.

Some places run a genuine self-responsibility system: duck the rope if you want, and if you need rescuing, you pay for it. Rusutsu is the clearest example, no marked tree zones at all, the whole East Mountain open, and you don't need a guide to enjoy most of it. Others grade zones for ability and name them individually, leaving you to ski them unsupervised once you're through the gate: Geto Kogen's tree runs work this way, each one rated and described, no guide required for the graded terrain itself. Appi Kogen sits in between: there's no go-anywhere policy, and one of its more serious tree zones is reserved for guests who buy a premium ticket or pay per run, but the resort has stopped enforcing the old rules elsewhere and won't stop you heading into the in-bounds trees across most of the mountain.

Then there's Kiroro, which keeps a much shorter leash: a handful of marked tree zones and a lot more roped off than somewhere like Rusutsu. The genuine backcountry beyond the resort boundary is a different question again, and that's where a guide stops being optional. Anywhere you're leaving the lift-served, in-bounds terrain, whether it's a gated backcountry zone or an unmarked peak, go with someone who knows it or don't go at all.

The practical rule: check the specific resort before you arrive, not Japan in general. If a guide is something you want regardless, book it as early as you book your hotel. The good English-speaking guides are usually close to fully booked for peak season well before most people start planning.