Snowy Owl is a Sanderson off-white — soft, pale and quiet — so the useful question isn't what 'goes with' it so much as what it should sit on top of. This is the light in your scheme; the character comes from the layers beneath it.
For a two-tone room, put Paint & Paper Library Slate IV (LRV 67.5) on the walls and Snowy Owl above — ceiling, cornice, trim. Slate IV is a warm grey-green with an olive, khaki lean, and it's clearly the deeper of the two, so let it do the colour work while Snowy Owl keeps everything airy. Run it the other way — Snowy Owl walls, Slate IV woodwork — and you get the smart, trim-deeper-than-walls look instead.
For the mid-depth note, Mylands Artichoke BH.13 (LRV 27.6) is a muted, earthy olive that's cracking on a cabinet run, a chimney breast or panelled lower walls with Snowy Owl above.
For the anchor, Dulux Sapphire Springs 1 (LRV 6.4) reads as a near-black slate-blue — ideal for window frames, a feature door or Crittall-style glazing. One properly dark line through all that softness makes the off-white look deliberate rather than default.
Because Slate IV and Artichoke pull the scheme warm and green, don't feel bound to cold metalwork — aged brass sits happily here, though nickel and chrome suit a crisper finish. Oak, linen and a wool rug stop pale walls feeling empty.
Practical advice: two coats on big A3 boards, viewed morning and evening and in the darkest corner of the room. Off-whites take their character from their neighbours — Snowy Owl will look white next to Slate IV and softer next to a brilliant white — so always judge it against what it'll actually live with.