When to come — and when to absolutely avoid
By season
Quietest: Mid-January to mid-March, and again all of November. Snow on the Great Parterre is breathtaking, the palace state rooms are warm and the queues at the Schloßstraße turnstile collapse to nothing. Cold (-3°C average in January) but the bare-tree silhouettes of the Gloriette against a winter sky are unforgettable.
Busiest: July and August, the Christmas Market weeks in December, and Easter weekend. Saturdays from May to September the palace can sell out its midday slots online the day before. Avoid the Austrian National Day (26 October) at Schönbrunn unless you're specifically there for the holiday crowds.
Best of both worlds: Late April–early June and mid-September–mid-October — gardens in full colour (tulips and roses in spring; copper foliage and the dahlia beds in autumn), palace doable at 09:30, and outside the peak coach window the Gloriette hill is calm.
By day of the week
Tuesday, Wednesday and Thursday are noticeably calmer than the weekend. Monday is fine but slightly busier because some Vienna museums close on Monday and tourists redirect to Schönbrunn. Saturday afternoon is the single busiest slot of the week — avoid it if you can.
By time of day
The first palace slot at 09:30 is by far the quietest of the day. Slots after 16:00 in summer are also markedly calmer than the 11:00–14:00 peak. For photos and the Gloriette view, the magic windows are sunrise (palace bathed in golden light from the front) and sunset (golden parterre lit from behind) — both free and both worth setting an alarm for.