You can explore the attractions in Budapest in a Segway Tour in the winter season too. The Budapest Segway Tours are available on Dec 24, though there are no tours on Dec 25 and 26.
You can check the available December tour dates and make your booking online in advance on Budapest Segway Tour.
Tours will go in windy and rainy weather conditions, but snow (if there is any snow fall at all in these mild winters of the last few years), may be a problem, which means you may have to re-schedule the tour.