Liechtenstein is worth visiting year-round, but what you get out of it depends heavily on the season.
Summer (June to August) is the most popular time. Hiking trails in the eastern mountains are fully open, the Rhine valley is green and warm, and the outdoor swimming pools are in use. Vaduz can feel busy on summer weekends, mostly with day-trippers from Switzerland. The highlight of the summer calendar is National Day on August 15, when the prince opens the castle grounds and the whole country has a party. Fireworks over Vaduz are worth staying for.
Spring (April to May) and autumn (September to October) are the best times for hiking without crowds. September is particularly good: the vineyards on the valley slopes turn gold, and the Vaduz Wine Festival brings local producers out for tastings and food.
Winter (December to March) works well if you want to ski at Malbun or simply want a quiet visit. The Christmas markets in Vaduz are modest but genuine. Snow on the valley floor is not guaranteed, but the mountains usually have good cover from January onwards.
One practical note: many restaurants, shops, and even some museums are closed on Sundays and sometimes Mondays. This applies more broadly outside Vaduz. Plan accordingly if you are visiting outside peak season.