Generally studless tires are best in situations where the roads do not have ice and the vehicle does not depend on friction for stability. For example bicycles depend on friction for stability but cars do not.
However, in practice you probably won't change your tires every day, so you have to estimate from the climate of the area whether studless or studded tires are better. For example, if the climate is such that there's a well-determined time when the winter starts, and the temperature during the winter is clearly far below 0 degrees Celsius and there's a well-determined time when the winter ends, you can expect that in the winter the roads are mostly free of ice and there's snow on the roads instead.
However, in climates where the temperature stays around zero for long periods of time, ice is very common.
I wouldn't use studless tires on a bicycle because the stability of the bicycle depends on friction.
Also consider this: on cars the usefulness of studless tires is based on the fact that many drivers choose studded tires. Thus, the drivers that chose studded tires make the ice rougher. So in areas that see lot of car traffic, the ice becomes soon very rough, thus friction with studless tires due to rough ice can be acceptable.
However, bicycle tires are very narrow, and there are very few bicyclists even during summer. In winter, bicycling falls approximately to zero. You are about the only bicyclist on the road if you choose to ride bike during the winter. Thus, because of the narrow tires and very few bicyclists, you can't rely on all areas of ice to become roughened from studded tire traffic.