Moses initially emigrated to the Great Salt Lake Valley in the 1849 Allen Taylor Company with his second wife, Mary Jane Sanderson Sanders; his step-daughter, Mary Louisa Sanderson; and his son, David Walker Sanders. The rest of his family came a year later in the 1850 Warren Foote Company.

Some secondary sources suggest that Moses participated in the 1856 rescue effort to help those stranded on the plains of Wyoming, however, further research and primary source documentation is needed in order to confirm his participation.