That is subjective because it depends on how much water you like to use and what diameter hose you are using, but one easy way to calculate it is to get a gallon container, turn on your hose to a pressure you like to use to bathe your horse and time how long it takes to fill the gallon container. Or to make the math easier, fill up a container for exactly 30 seconds or one minute (depending on how large your container is), and you will know how many gallons per minute you will need. I have only heard of wells being measured in gallons per minute, but it's just a math difference.
I just did this because my well is not a very high producer and I wondered if it will be sufficient for my needs. My memory is so bad -- I just did this about three days ago -- but I think I came up with about only a gallon and a half a minute being a nice pressure -- again, I can't really remember except that my well will be fine. I used the faucet in my laundry room and filled a gallon container. Good luck.
Out of a 3/4" water hose, normal size is 5/8, I like at least 7 gpm. GPH is a pretty weird measure for hose flow. Not over 4 or 5 gpm, and I'd use a 5/8 hose. Flow and pressure at the faucet is varied some at the end of a hose, so if you have less than 5 gpm, there is too much pressure drop for my taste at the end of a 3/4 hose. For me, more flow rate is better.
Time how long it takes for any hose to fill up a five gallon bucket, and you can figure what your flow rate is.