If we're really lucky, the consequences will be minimal: spiders and other predators will simply find something else to eat. But if mosquitoes had some heretofore undiscovered critical purpose for the environment, we might have seriously screwed things up.
Aedes aegypti did not exist at all in Fresno, for example, until 2013.
These species of insects were introduced to these ecosystems. By humans. The diseases (for example, Zika) being spread now are the consequences of us introducing these mosquitoes in the first place.
You are mistaken. Not wiping out all mosquitos, just the specific aedes aegypti species from the aedes genus.
But what if mosquitoes are actually bad for the environment? By not removing them we can be screwing things up!
And it sure isn't unknowable - find what is interacting with that mosquito (something may be eating its larvae or reproducing symbiotically or parasitically etc). That dependent creature will be catastrophically affected, likely become extinct as well.
This problem has been studied: https://www.nature.com/news/2010/100721/pdf/466432a.pdf