One of the major nonprice determinants of demand is consumer tastes. When consumer tastes change, the demand for various goods changes along with them. These changes can be essentially impossible to predict or explain. Sometimes they are driven by things like celebrity endorsements. Other times, there is simply no clear reason.
In the case of small cars, an increase in their popularity will clearly lead to an increase in the demand for them. Demand is defined a schedule of the amount of a particular good or service that consumers will be willing and able to buy at any given price. If demand rises, it means that people will buy more of the good even if the price does not change. It can also (depending on how much demand rises) mean that they will buy more of the good even though the price of the good rises. This is what will happen if small cars suddenly become popular. Demand for cars like the Mini Cooper and the Smart Car will increase. More people will be willing to buy them even if the price does not change or, perhaps, even if the price increases.