how do i figure out if my pasture grass will survive treatment from broadleaf weed killer
It is difficult to answer your question without identifying the forage grass in your pasture. Check with your county Extension office to see if they can assist you in identifying your pasture grass.
Then check the herbicide label for restrictions on new seedings and established stands. Most pasture herbicides have restrictions on spraying new seedings that call for new grass seedlings to be a certain height/growth stage before it's safe to apply herbicide.
It sounds like this is an established pasture, so best to check with your county Extension Office to identify the pasture grass before spraying.