Wenzel was born in Großschönau (Kingdom of Saxony) in December 1863 as the son of the damask weaver and amateur musician Carl Gottfried Wenzel. His musical talent was already evident in his youth when he joined the church choir at the age of eleven. The cantor of his hometown recognized this talent and taught him counterpoint and organ playing. Soon he was able to substitute for his teacher on the organ. At first he attended the so-called weaving school in Großschönau and learned his father's profession. Due to financial reasons it was only possible for him to start studying music at the age of 21. He entered the Dresden Conservatory. There he received a thorough education in piano and violin playing, singing, harmony and composition, the latter with Felix Draeseke. After his studies he returned to his home town in 1887 and settled down as a freelance music teacher, choirmaster and composer.