Hi Anne,
This route can be a tad tricky to plan but is well worth the effort in my option. You can two options to travel from Matsumoto to Kanazawa. One is indeed via Nagano the other is via Nagoya, both places make for a good day visit. Perhaps you could plan a nights stay at one of these if you feel that the trip is too long for a single day.
Try to avoid local trains if you decide on making the trip. They can be rather uncomfortable for longer distances, especially with Luggage. Please see this link and take a look at Route 2. This route is via Nagano and you can travel the whole trip in limited express trains that are very comfortable well worth the ride alone. This may be the only option that uses limited express trains on this route so plan carefully if you want to travel via Nagano. It is also one of the fastest route available by JR.
The last time that I made a similar I traveled via Nagoya, for this route please see route 4. The nice thing about this route is that it only involves one transfer at Nagoya and you can spend a couple of hours in the city before your taking the next train and the part from Matsumoto to Nagoya on the Wide View train is one of the most scenic routes in Japan.
Both routes do take around 5-6 hours, so brining a book or a hand held is a good idea to pass some of the time.
I hope this helps!
-Daniel
