My wife and I boarded the train in Wernigrode last fall for the trip and had a wondeful time. We rode in late October. The temperature at the top was quite cold at that time of the year. Your children should love this trip as all the trains are steam powered.

You can get off at the top where there is a restaurant. Many people were hiking at the top. The views were magnificant. I highly recommend this. In fact, I plan to return to take the train in the winter.

If you are in the area, yes, go for it. To entertain the kids, collect some of the regional legends and fairy tales to tell them on the way. Brocken is the legendary Blocksberg where the witches go to dance on Walpurgis night (April 30/May 1)...

Pick a day with good weather if you can.

I have been up twice within one week, in late November with the first snow. Conditions were the two possible extremes. Trip 1 was done with the winter forest in purely magical splendour but the mountain top in clouds, a snowstorm, hoarfrost with needles of 5 cm or more length (I learned that day that hoarfrost crystals grow against the wind!), maybe 50 metres visibility and hardly anyone else going up - no view, but it was special and unforgettable. I only located the summit because of the brass arrows in the rocky ground that pointed in all directions to places I was supposed to see. Ha!
The second trip, less than a week later, took place on the sunniest and clearest of winter days with a view over 150 kms, over to the peaks of Sauerland and Thüringer Wald. I was able to locate the suburb of Braunschweig where my parents live, 50 kms away. It felt like being on top of the world, as the Brocken is the highest elevation in the whole of North Germany.

You'll also like the small town of Wernigerode with its half-timbered houses and the little castle.