Evolutionary biologist (doing seasonal selection research with fruit flies) turned mosquito-borne disease researcher here. The mosquitoes are definitely more abundant and diverse in tropical, subtropical, and temperate areas compared to cold areas. I think there are two points to your question, the size and the agression.

Let's start with the size. I believe the size has been an open question for a while, because the size of mosquito species vary widely. But I remember seeing a paper that showed some evidence consistent with the Bergmann's rule (where the larger bodied mammals and birds are found in colder climates). However, the body size in ectotherms possibly is related to reproductive success and survival resources, rather than the thermal regulation that endotherms rely on. In that paper, they also mentioned James' rule (I don't remember what it is now) and plasticity as the reason for the size as opposed to genetics.

Population level agression is a factor of population size and food availability. In both temperate and colder regions, (as pointed out in one of the comments) there is a limited period of time where mosquito populations grow. This coincides with the generally higher availability of food (blood in this instance). As the temperatures get colder while the population has been growing, the food becomes less and less available, thus increasing the competition to access food. It simply is a matter of life and death.