So, while looking thru my "Weeds of Nebraska" book this morning, I discovered that when you say "horseweed", you could be referring to this:

http://www.illinoiswildflowers.info/weeds/plants/giant_ragweed.htm

or this:

http://wisplants.uwsp.edu/scripts/Detail.asp?spcode=IVAXAN

or this:

http://www.illinoiswildflowers.info/weeds/plants/horseweed.htm

It's enough to drive a guy crazy.......

(I like it when we standardize weed names- everyone agrees on the same name.)