I first installed a tankless propane in a off-grid (solar panels, battery back up), cabin in the Mts of Colorado in the early 90s. Worked well for a couple of people taking a showers with low water pressure and for the sink hot water needs.
I would like to believe they have come a long way in almost 30 years. The cost of one is dictated by needs, water pressure, the temp of the incoming water etc. There are very good websites that will walk you through the “math” tp size the model to your needs. But I think you will find they are pretty pricey.
The electric models are limited on what they can do. Esp the 120 verse 220 volt models. The are mainly designed for point of use, like a sink that uses low flow water pressure. I think most horse people like pretty strong water pressure when it comes to washing horses. They can’t keep up with that demand. Esp if incoming water temps are in the 40s-50s. Though I was thinking, wondering if hooking up 2 in series would change things? First one boast it to around 60-70 and the second one up to 100++
If washing more than 1 horse in any given hour. I think a 30 gallon conventional water heater may/will run out and you’ll have to wait for it to recharge. I installed an 80 gallon electric tank. Insulated well and put a timer on it. Mechanical utility timers cost around $40+ and are easy to hook up. The majority of our use for 5-10 horses was in the mornings. It started heating water an hour before use. Shut off about a hour after our usual morning routine. Still held the water temps for needed for the rest of the day. So on average it was only heating water for 4-5 hours a day. The timer boxes have a switch to turn it on when needed. You can get additional on-off “switches” for a couple of $ to have multiple time periods if needed. Or spend big bucks for a digital programmable timer.
Propane heaters tend to be more economical than electric. Depends on the supply cost of each. If 220 is close and easy to run a wire. Electric water heaters are cheaper than gas. Very simple to hook up. Not that propane is that hard. In my area the propane supplier with a contract will do all the hook up for free.
That’s the basic long of things. IMO go with a conventional water heater for barn use. Don’t think you can get a timer for a gas heater? So you are heating, keeping water hot all the time. Verses an electric with a timer.