Day trip from Cologne to Amsterdam?

Doable? Yes.

But, the fastest trains take a bit under three hours, so it's a lot of travel for a day and in my opinion not worth it.

Not exactly from Cologne but close enough , from ( by train ) Düsseldorf to Utrecht, transferred to a bus to Doorn. Came back in the early evening. Well worth it as to time and effort.

Certainly your day trip is doable logistically. I did this in the summer as I only go over in the summer, one reason more day light. Worth it...depends how desperate you are to see what you want in Amsterdam.

Aachen or Düsseldorf might be more practical. Amsterdam has so many direct flights that it might be better to incorporate it into your next European vacation. Also consider Monschau, more touristy but very attractive.