Ice out is not the factor which determines emergence for BF's and mozzies.
Black flies in the north are larvae and pupae in rivers, and emerge from their pupae in rivers, based on water temperature, and they over-wintered as larvae/pupae, so they are ready to go. The first hatch is usually somewhere between 10-12 deg C, depending on the species. the more they research it, the more variation they find. So your local lake could be ice covered, but if the streams are open and 10-12C, the first hatch is on.
Mosquitoes have several modes of appearing depending on species. Some over-winter as adults, so they can be out when the lakes are frozen as soon as it warms up, including when there is still snow on the ground if its really hot out. But most over winter as eggs, and they hatch into larvae, then go to pupae in a matter of days to a couple of weeks. Again you can have ice covered lakes, but mozzies mostly come from fish-free shallow pools in the woods, and in your rain barrel, old tires, and puddles behind buildings and in fields. These heat up very fast and produce hatches independent of the lake ice.
Open lake water does not produce many mozzies because of wave energy, and because fish and other invertebrates (e.g. dragonflies nymphs) which graze on mozzie larvae which are easy pickings from the water surface. Grassy inlets that melt out first may be big mozzie producers. But that's food for all the critters (amphibians, dragonflies and other insects, fish, birds, bats, etc).
Dress properly, and DEET is your friend.

There is no need to miss any of the season due to flies.