Catalyzes formation of 5-hydroxymethyldeoxyuridylate (5HMdUMP) as a step in the pathway that replaces dTMP by thymidine hypermodifications in the viral genome (PubMed:8527927). As a final result of the pathway of hypermodification, hydroxymethyluracil substitutes for a subset of thymidines in the viral DNA (PubMed:8527927). These modifications probably prevent degradation of viral DNA by the host restriction-modification antiviral defense system (PubMed:8527927, PubMed:21597187). (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + dUMP + H2O = (6S)-5,6,7,8-tetrahydrofolate + 5-hydroxymethyl-dUMP Homodimer. Belongs to the thymidylate synthase family.