On the trains, as a rule, no.

It is available, though, on a small number of trains between Moscow, Saint Petersburg, Nizhny Novgorod and Helsinki such as the Allegro and Sapsan rail services. The number of routes, and services, on which Wi-Fi is available is increasing all the time.

It is increasingly available in stations though, with almost all major railway stations in Russia now covered. Many do have a sign-up gateway in Russian though, so if you enter any personal details to gain access, be careful you know what you are signing up for.