Broadreach is building Wi-Fi hot spots in 20 stations along Virgin's west coast rail line in the U.K.: The hot spots will just cover the stations. The article says the network will "likely" use satellite for the downstream and cellular for the up. The operator of the east coast line in the U.K., GNER, is also building hot spots over its stations.
Busy train lines in the U.S. should be working on this too. One in San Jose already is, but I haven't heard of any Wi-Fi coverage over lines on the east coast along busy corridors around Washington, D.C., or New York.