If you are visiting in winter, bundle up for the playground. The kids will want to play for hours, but it will be cold.
There are lots of stairs in the castle and it is enormous, so prepare the kids to walk a lot. You can bribe them to keep going with the playroom at the end of the tour.
In the summer, visit the castle in the morning to avoid lines and crowds. Having the castle virtually to yourself is an incredible experience. In winter there are hardly any visitors.
The castle and playground are open all year. However, summer is certainly more pleasant to be outside. Most of the castle experience is indoors so you will be comfortable. The castle has a cloakroom to drop-off large coats if needed.
Children under four are free at the museum.