Absolutely, and the mundane details you are hesitant to share are often exactly what inmates appreciate most.
Life inside is stripped of everything ordinary. The same walls, the same faces, the same routine day after day creates a kind of sensory and experiential deprivation that makes the normal details of outside life feel genuinely meaningful rather than trivial. A new dog, a Christmas gathering, what the weather has been like, a funny thing that happened at the grocery store, all of it lands differently when you are cut off from that world entirely.
Mail call is one of the highlights of the day in any correctional facility. Having your name called, receiving an envelope, and sitting down to read something from someone who cares enough to write is a real and significant event in a day that otherwise offers very little. The content does not need to be dramatic or important. The fact that someone took the time to write is the point.
Send the letter and include photos of the new dog. A picture of a dog at Christmas is the kind of thing that gets pinned up in a cell and looked at every day. If you want to make the first one easy and affordable, email aid@inmateaid.com and ask about a coupon for a first-time send. InmateAid can get the letter and photos to your nephew with your home address kept off the envelope entirely.
Do not wait for good news to write. The ordinary stuff is the good news.