Travelling 24-29 Dec: Any transport problem?

I would be on a lone trip arriving 24 Dec and departing 29 Dec. Itinerary Narita --Matsumoto ---Nagano ---- Tokyo --- Narita.

Could I ask if there would be any problems getting train tickets during this period?

Thank you!

There could be problems if you are trying to reserve tickets for the Shinkansen or buses because you are competing with all of the New Years travelers. Also, Christmas weekend is a 3 day weekend, so many people are traveling which means Christmas day may be a little crowded although I don't think that day will be so bad.

Should be no problem for buying JR train tickets all along the way back to Narita.

I guess your train route is:

Narita airport - Shinjuku - Matsumoto, - Nagano, - Tokyo station - Narita airport

It's all JR. Nagano-Tokyo is bullet train ride.

The real rush does not start until the 29th, so you should not encounter any extreme situations. On the afternoon and evening of the 25th the trains into Tokyo might be pretty crowded, but not extreme. On the 29th the trains to the airport could be rather busy, but if you make an advance reservation you should be able to circumvent any problems:
http://jreast-shinkansen-reservation.eki-net.com/