Catalyzes the 2 serial methylation steps for the conversion of the 7-monomethylguanosine (m(7G caps of snRNAs and snoRNAs to a 2,2,7-trimethylguanosine (m(2,2,7G cap structure. The enzyme is specific for guanine, and N7 methylation must precede N2 methylation. Hypermethylation of the m7G cap of U snRNAs leads to their concentration in nuclear foci, their colocalization with coilin and the formation of canonical Cajal bodies (CBs. Plays a role in transcriptional regulation.