Horseshoes for horses are mild steel. They weld just fine. There is a whole industry of horseshoe knick knacks, including coat racks, andirons, goofy little cowboy candlesticks, and so on.
Horseshoes for pitching are made of all kinds of stuff- some of em probably are cast iron, some are aluminum, I have a zamac one sitting around, and I have seen plastic ones too.
Racing horseshoes are aluminum- I had a friend at the track give me a bucket of em, but I never did anything with em.
First you gotta figure out what yours are- then, if they are indeed cast iron, tig brazing is probably the best bet. Easy, quick, no preheating or post weld slow anneal.