For most travellers, summer is the right time. From May to September the old town is open, the gardens at the Münster are in flower, and the test tower platform gives reliable visibility for fifty kilometres.
The big exception is the week before Lent, when the Rottweiler Fasnet is on. If you want to see the Narrensprung — and it is one of the most striking living folk traditions in Europe — that means Fasnetsmontag, the Monday before Ash Wednesday, in February. Book accommodation many months ahead; the town doubles in size for the day.
Winter is otherwise quiet, with most museums on shorter hours and the streets often dusted with snow.