Short Answer: Not necessarily.
Long Answer: Sake has been a staple beverage in Japan for many hundreds of years. Prior to the 20th century, sake was generally a much rougher, grainier drink and taste “flaws” were more apparent in the beverage. Thus, warming a tokkuri of sake was considered the only way to serve it for the common man. There were some sakagura that made a superior sake but it was reserved for the more affluent members of society. As the fermentation process has evolved and been refined, on aggregate sake has become a cleaner, more delicate product. Think about wine made from grapes. They generally tell you to chill white wines prior to serving, but do you think that was the case prior to refrigeration?
Throughout its existence, sake has been served at temperatures ranging from just above freezing (referred to as reishu) all the way to steaming hot (referred to as kanzake). The warmer the sake is served, the more flavorful and drier the flavor will become, while chilling it will open up the bouquet of the sake as well as give it a crisper flavor.
There are two major factors in deciding whether to heat, chill, or serve your sake at room temperature. The first is food pairing. Simple flavored foods like sushi or sashimi are paired well with kanzake as well as fatty and oily dishes (like hot pot dishes). Particularly sharp flavored food, like sweet and sour dishes, are best paired with reishu. If you aren’t drinking with food you can drink it either way!
The second factor in deciding on a temperature is quality of the sake. Higher quality sake have multi-leveled, very nuanced flavors that can be overpowered and lost when heated. Heating these quality sakes would be like drowning filet mignon in ketchup. Lower quality sake isn’t necessarily going to be bad, but I can attest that warming these sakes definitely improves the flavor (and makes your cheeks very red).