This is an interesting topic brought to my attention by a researcher studying, of all things, mosquitoes biting frogs! I have a small collection of such events, but I will look for more now that I am "tuned in".
I believe that my frogs generally go for bigger prey than mosquitoes. (See the food chain page for bullfrog dining adventures.)
These shots beg further questions... why have I never seen a mosquito on a spring peeper? Or a mosquito on a gray treefrog? Do mosquitoes bite the exposed skin-parts of turtles? They surely bite ME when I am out there at night!