Hello!!
I'm heading over the first week of January and I was just wondering what to expect weather wise during my trip. Also, any suggestions on must see's or fun outings for a group in their mid 20s...Thanks for the insight :)
The first week of Jan for Amsterdam would not be by first, or even third or fourth choices. The days will be short, overcast, damp, cold with rain and snow or could be decent but the odds favor marginal weather. Weather will be/can be a major factor for what is available at that time. It will be most indoors, museums, Anne Frank house, etc.
Weather will be similar in all three cities that you have posted about - London, Paris, and Amsterdam. Before leaving the hotel in the morning, I check the latest forecast on weather.com or their app.