The Dreadhorde deck's mana base isn't even that bad to be honest.

17 green lands is plenty to start casting all your creatures.
17 black sources is easily enough to cast Dreadhorde (13 lands, 4 Paradise Druid)

All the non-BG cards are castable off Interplanar Beacon. The list has 11+4 blue sources, 8+4 white sources, and 6+4 red sources, which is slightly low on a few counters, but it's not like you have a ton of cards that require any of these colours, and a full set of explore creatures helps you to get whatever colour of mana you need pretty easily.

I've played greedier mana bases in Legacy.