Cosmo Clock 21
Banned
Is it possible to take on some of the more difficult dungeons with Horus and just a team of non-REM monsters? I don't want spend money.
Depends on how late game you consider "difficult". I just steamrolled Master Skydragon with this team:
The only IAP asides from Horus on that team is Neptune, who you could substitute the non-IAP Hera-Is in for. It's also a team that's the product of about six months of play, so you might also want to ask yourself when you want to tackle the more difficult content.
Most of the Descended dungeons have a poverty team which can 0 or low-stone it with farmable monsters. Hell, even Valkyrie, once considered the hardest dungeon in the entire game, now has non-IAP strategies available.