It depends on the type of mochi. Kinako-mochi (soybean flour mochi), kagami-mochi ("mirror mochi") & hanabira-mochi (flower petal mochi) are eaten during the New Year's celebration.
Sakura-mochi (cherry blossom mochi), hishi-mochi (water chestnut mochi) & kusa-mochi (grass-mochi) are eaten in the spring.