Ash seedlings have been prolific this year. Male ash trees do not produce seeds, so you or a neighbor has a female ash tree that produced seeds last fall.

Hand pulling these seedlings from garden and bed areas is the safest way to get rid of them, but requires some time and diligence. You could also cut them down with grass shears to remove the leaves. Glyphosate (Roundup® is the most common) can be applied to the leaves, however, do not get the herbicide on any desired plants in your landscape. Spray on a morning with no breeze to avoid herbicide drift. Always follow label instructions when using herbicides. Finally, make sure beds and borders are thickly mulched in order to help hinder sprouting of seeds and other such non-desirables.

For lawns, keeping a healthy, thick, vigorous lawn will help. Regular mowing will eventually get rid of the ash seedlings, however, do not adjust the mowing height just to cut the seedlings in the lawn. The preferred mowing height for Colorado lawns is 2.5 to 3 inches. Mowing to less than 2 inches can result in decreased drought and heat tolerance and higher incidence of insects, diseases and weeds. Herbicides for lawn weeds (such as Weed B Gon®) can also be used, but again, always follow label instructions when using herbicides.

Lawn care fact sheet:

http://extension.colostate.edu/topic-areas/yard-garden/lawn-care-7-202/

Pesticide information:

http://extension.colostate.edu/docs/pubs/garden/xcm220.pdf

Samaras (winged seeds) may remain on female ash trees until winds knock them down. 

The only possible "seed/fruit preventer" is ethephon, sold as Florel.  While the label does not mention ash specifically, you could have a tree service spray female ash trees as a trial.   It would have to be applied during flowering in April.

All that said, the nuisance seeding and allergic reactions would tend to make these trees less desirable to you....consider having them removed and replaced with something other than ash.