Horseshoe on rope?
The best answer I can come up with is "it all depends!"
If you want to use it as a floatation device to throw to a hapless crewmember until you can get back to them then a rope/line is not needed.
If you have a man overboard pole you plan to throw over with the horseshoe the two should be attached to each other with a line. A man overboard pole, if you aren''t familiar with the term, is a device similar to a fishing pole that floats upright in the water. It usually has a flag attached to the upper end to help the boat locate the crewperson in rough water when it might be hard to spot a head bobbing just above the surface. A floating line is easy to see and grab if you are in the water. It also keeps the line away from the prop when you are manuovering to pick up the MOB.
If you want to use the horseshoe with maybe a 100'' of floating line attached to the boat, you can throw it overboard and then circle around the MOB until he can grab the line/horseshoe. With the boat stopped, you can then pull the MOB back to the boat with the line.