We will be visiting our daughter in cologne. In addition to seeing the cathedral and visit some Christmas markets we would like to do some outdoor activities. We are big hikers. Any recommendation of snow shoe, cross country ski, other outdoor activities for winter. Planning on using public transportation. Thanks.
December is usually not snowy, but drizzly, cold and grey - just to make sure you are not going to be disappointed. Proper cold with snow does frequently not happen until January.
Anyway: Is the Black Forest a fixed point already, or just a spot you thought about for hiking etc? If the latter is the case, there are other suitable areas that are probably easier to get to - some „Mittelgebirge“ (low mountain range, like Black Forest) are substantially closer. These mountains usually have the best chances of being white to a certain degree, and which does is hard to predict.
We have no fixed itinerary yet.
I once spent 4 nights in Titisee two weeks before christmas, very cold with clear blue skies but no snow and no sign of any winter sports businesses getting ready. Dropped through the low cloud on the way down to Freiburg where it was just plain miserable.
Cologne is a long way from Black Forest, I'd change one of those - but since you can't change your daughter it will have ot be the mountains.
Easiest from Cologne is probably the Eifel range. They seem to have most of what you mentioned, but I have never been there in the winter.
Another question: When in December are you going to be in Germany? Note that most markets will have closed by Christmas Eve. Only few exceptions I know of: Goslar near the Harz mountains, and Baden-Baden near the Black Forest. Both regions are nice for outdoor and you need about the same time to get there from Cologne (3-4 hrs by train). I have been to both regions, but due to the infamous Christmas Warmth Period that is very common in Germany, without snow.
Other, closer options are Taunus near Frankfurt, Westerwald and Hunsrueck (all close to Cologne). I lack knowledge of these, though. Presumably there are more knowledgeable people on the forum…
I would want to be in a city of some size that is near good hiking options; setting up in a remote town in winter could prove disappointing it the weather isn't cooperative and you can't hike.
The Hunsrück was mentioned, an interesting area that is sandwiched in between the Rhine and Mosel Rivers, one that few people have heard of and which indeed is not far from Cologne, but it is one of the weakest areas when it comes to public transportation. There is an airport there, Frankfurt Hahn, in the middle of nowhere, but train service is possible only on the periphery, and bus travel there is usually slow... I would suggest staying in KOBLENZ if this area interests you. Koblenz is south of Cologne on the main Rhine River Railway where the Rhine and Mosel Rivers meet up, an easy move by direct train.
Find Hunsrück hikes at the Komoot website.
https://www.komoot.com/guide/113/hiking-in-the-hunsrueck
Bus 620 gets you from Koblenz into the Hunsrück region.
Koblenz is a major train hub which sends off trains up the neighboring river valleys to places of interest... the towns of the Mosel Valley, the Upper Middle Rhine Valley, and the Lahn River Valley. All of these river valleys have good hiking options. Check Komoot,
https://www.mosel-inside.de/en/travel-guide/mosel-villages.html
https://www.mittelrheinentdecken.de/en/
https://en.hessen-tourismus.de/where-to-go/regions/lahntal
I have spent a fair amount of time doing hikes in the Mosel an Middle Rhine Valleys. Many hikes follow the cliffsides as you move from one town to the next, providing great views. Have a close look at the Rhine Castle Trail and the Rheinsteig Trail, the main routes along the two Rhine banks.
https://www.komoot.com/collection/721/the-rhine-castle-trail-13-stages-of-pure-rhine-romanticism
https://www.saarfuchs.com/wp-content/uploads/2024/03/top-14-premiumwanderwege-4.jpg
https://www.komoot.com/collection/776/rheinsteig-trail-the-21-stages-along-the-rhine
Marksburg Castle, in Braubach, just south of Koblenz, on the Rheinsteig Trail, can be toured and is open year round.
The riverside towns are all well served by train, which makes it easy to return to Koblenz. And if hiking is not possible, check out Koblenz itself, Trier, Limburg, Mainz, Wiesbaden, Remagen, and the other interesting towns and cities within easy reach of Koblenz.