I have spoken to our water quality specialist at the County. The photos that were provided - which were very helpful! Are a common duckweed. That level of surface vegetation makes it HIGHLY unlikely that any algae exists in the ponds.

That being said - two pups were extremely sick after swimming in them, which is likely due to some sort of micro-organism in the water, which we are unable to test for. Some dogs may get sick from it, others may not.

Those ponds are not very deep, and are not monitored for water quality. Which makes them subject to water quality issues. So please use them at your own risk. If you have any further questions, please let me know.

Jennifer Fink
Recreation Services Supervisor
Ramsey County

Blue Green Algae warnings come around every summer, but it appears the problem with blue-green algae is much more pronounced this year. BC regulars will recognize the common duckweed, which is not a problem. What you should look for a bright green scum on the water (almost like paint).  Here is some more info from the MN Pollution Control Agency: 

Summertime in Minnesota: When in doubt, best keep out!
When temperatures climb and the summer sun beats down, conditions are ripe for Minnesota lakes to produce harmful algae blooms, some of which can be harmful to pets and humans.

What: Harmful algal blooms (HAB) are blue-green (cyanobacterial) algal blooms containing toxins or other noxious chemicals, which can pose harmful health risks.

Why is this a concern? People or animals may develop skin irritation or upper respiratory problems from exposure to HAB, and in extreme cases, dogs and other animals have even died after drinking lake water containing these toxins.

Where: Severe blue-green algal blooms typically occur on lakes with poor water quality (high in nutrients), and look like green paint, pea soup, or a thick green cake (see photo gallery below for examples). HAB often result in extremely low water clarity (less than 1 foot). There is no visual way to predict the toxicity of an algal bloom

What should I do if I suspect a HAB on my lake? When these conditions are present, people should avoid contact with the water and they should prevent animals from swimming in or drinking the water. Scientists do not yet know what causes some blooms to produce toxins while others do not, so the safest course of action is to avoid contact with all blue-green blooms.

What does it look like? Blue-green algae can be hard to distinguish from other types of algae. While it's often described as looking like pea soup or spilled green paint, it can take other forms as well.  The photos on their website show some of the diversity of blue-green's appearances and also provides some examples of other types of algae or plants that may be mistaken for blue-green algae.

http://www.pca.state.mn.us/index.php/water/water-types-and-programs/surface-water/lakes/blue-green-algae-and-harmful-algal-blooms.html