In Vienna the Christmas presents come from the Christkind, the Christ Child, and in December children can write their letters to it at a desk inside City Hall, beside tables where they decorate gingerbread. Much of Vienna in December is that easy with children, and a good deal of it is free. The weather and the crowds take more managing. The days are short and the waits at tram stops are cold, and on weekend evenings the popular markets are shoulder to shoulder.
The desk and the gingerbread are in the Volkshalle, part of the Christmas market on Rathausplatz, which packs up on 26 December. The children's ice area in Rathauspark next door is free as well, and lends helmets and double-runner skates, so a small child can try the ice without you hiring kit. The programme changes from year to year, so check before promising anything. Go in the morning or on a weekday afternoon. Friday and Saturday evenings are the crush, and Spittelberg is worse. Its lanes are narrow, and on a Saturday night there is no room for a pushchair.
Plan each day backwards from the dark, which comes before five. Get the outdoor sightseeing done before lunch and keep the afternoon for somewhere warm, then go to a market at dusk, when the children's punch stands, serving hot non-alcoholic drinks, are hard to walk past. Thermal layers and waterproof boots matter more than anything smart, and carry spare gloves for anyone going on the ice.
The ball season formally opens on 11 November, but the big nights fall in January and February, and they are formal and late. The family version is New Year's Eve on the Silvesterpfad, the free trail of stages through the Innere Stadt. In the afternoon there is a children's programme, and on the Graben the city's dance schools run crash courses in the waltz. Take the lesson while the Graben is still easy with a pushchair, and be back at your hotel before the old town fills up for midnight.
Save Schönbrunn for the days after Christmas. The market in the palace forecourt turns into a New Year market after the 26th and runs into early January, well after most of the smaller markets have closed, and children can make decorations and cards in its craft hut while you look round the stalls.