Hey there Foxy, I pulled this from the wiki just to have the extra info,

“Horse care is made up of feed (+20% health per feed) for 3 bits, water (+30% health) for 1 bit, and groom (+10% health) for 6 bits. Feed and water are both required to breed, train, and show. However, grooming is not required, but reduces the random variable during breeding for BS from +/-6 from the parents average to +/-4."

All together the 3 care options are 10 bits.  This can be covered by careers (since horses can do 5 a day), winning low tier disc shows (can compete 10 times a day), and usually easily by winning halter shows (5 a day).   Of course you pick one or a mix to do during the day, but your daily care fees are pretty easily covered with having your horses in appropriate pathways for them.   If you need some extra cash you could always go play in the game room for an extra 100 bits per win (1 win covers care for 10 horses, you can find by clicking town and looking under the map).   

Other money options are exploring the plains and selling dyes / items, auctioning wild horses, etc.    Or exploring the mines and selling gems.   There are 2 guides in forums that include more ways to make bits if thats an issue for you (I will link those in a bit).  

Most games have either a small fee for care or they require you to go buy things like feed + groom tools.   HoFa just went the small daily fee route.    

In case these can help

This guide is in game for making bits (made by maki): https://horsefable.com/topic/6652?page=2 
This guide is on a google site (made by me) that has a page for making bits: https://sites.google.com/view/ineedapayraise/help-guides/guide-making-bits