Not true at all -- with Magnus you don't need horses (or iron) to build your units. For reference I highly recommend civtrader6 's videos. His Mongol deity game is great fun - no horses - no problem.
The only caveat being they won’t heal (except via promotion) until you secure a source . . . so all it takes is one of your neighbors having the missing resource for you to take.
Yeah, I am really enjoying his Mongol playthrough. Civtrader6 is awesome.