Garden plots- Do i have to take all the dirt out and put new dirt in?

Well think about it, what do horses eat? If it were me, I would till it over, add good compost and smother the weeds with newspaper, cardboard or landscape fabric.

Go to your local neighborhood garden center not a big box store. Take a sample of your soil. Most likely it is not balanced. Too much horse manure is too hot.

Any Manure must be composted over a period of time....turn the garden over, remove the weeds, add line, peat moss and garden soil.Mix it together ,allow to sit awhile before planting

If the horse manure you used was from animals that grazed in an open pasture... you may have brought the weed seeds into the garden.... you may have to replace the soil with new to get rid of them, especially if you let them go to seed rather than pulling them... Most commercial manure fertilizers are treated to eliminate weeds seeds... so use that instead of untreated stuff... Ask your LOCAL nursery... they may have other solutions for you.

I would remove all the soil and replace it with a soilless mix (google the recipe) that should cut down the number of weeds.

Thanks everyone for the answer. I will try it.