The website timeanddate.com is very helpful when you're wondering what sort of weather you might have on a day-to-day basis during your period of travel. It has weather data going back at least ten years for just about every potential destination of reasonable size.
Copenhagen weather -- October 2025
Use the pull-down box at the right, just above the graph to display statistics for October in other years. There can be a lot of year-to-year variation, so I like to look at the most recent five years.
Use the Search box at the upper right to see data for other cities and towns.
For precipitation, which seems harder to predict than temperatures, I usually just look at the monthly-average data in a city's Wikipedia entry. Even in southern Europe, it can get noticeably rainier in October, but it might still be dry for you.
One thing to keep in mind is how short the days will be in northern Europe at the time of your trip. That will reduce the number of effective sightseeing hours per day in rural areas, which might affect where you choose to spend some of your time. I was all set to suggest you take the overnight ferry to Oslo, then--a day or two later--set off on the Norway in a Nutshell route through fjord country to Bergen. There are non-stop flights from Bergen to Amsterdam (but check to be sure your travel date has that connection). However, upon reflection I'm not sure that's a great idea in October. How much of the scenery would you miss due to darkness? Is the risk of rain/fog high enough to make the (not inexpensive) Nutshell route ill-advised in October? I do not know the answers to those questions, but I missed the Stockholm Archipelago scenery when I took an 8 PM ferry from Stockholm to Helsinki in August a few years ago.
I haven't been to Copenhagen for over 50(!) years, so I am ill-positioned to suggest specific additional urban stops that would add variety to your itinerary. However, I've been to the other Scandinavian countries recently and found Oslo to be an attractive, interesting city with many good indoor sights (in case you're unlucky with the weather). Other urban destinations would be Gothenburg and Stockholm in Sweden. The smaller town of Lund (also Sweden) is a nice option if you don't want to hop from one major city to another. Lund isn't very far from Copenhagen.
